A FEASIBILITY STUDY ON THE
THREE-DIMENSIONAL
RECONSTRUCTION OF HIGH
VOLTAGE AND LIGHTNING
DISCHARGE CHANNELS USING
DIGITAL IMAGES
Yu-Chieh (Jessie) Liu
A dissertation submitted to the Faculty of Engineering and the Built Environment,
University of the Witwatersrand, Johannesburg, in fulfilment of the requirements
for the degree of Master of Science in Engineering.
Johannesburg, 2012
Declaration
I declare that this dissertation is my own, unaided work, other than where specif-
ically acknowledged. It is being submitted for the degree of Master of Science in
Engineering in the University of the Witwatersrand, Johannesburg. It has not been
submitted before for any degree or examination in any other university.
Signed this day of 2012
Yu-Chieh (Jessie) Liu
To my loving parents for allowing me to spread my wings.
To Tim, my supportive and unwavering rock.
iii
Abstract
The work presented extends and contributes to research in the visualisation of
discharge channels with an expectation to extend to lightning channels. Although
previous work in this area has produced three-dimensional (3D) information of
discharge channels, there has not been a method to visualise the channel and
the characteristics of its shape in a 3D environment. In the research presented,
photographed discharge channels are reconstructed in a virtual interactive 3D envi-
ronment.
It is found that single-channelled discharges produce models that correctly follow the
inferred channel paths from the photograph datasets. Single-channelled discharges
have also been verified in the controlled laboratory environment, providing confi-
dence in the two-image reconstruction algorithm. The algorithm is shown to fail
for an angular separation of cameras less than 15◦, which produces thicker channel
segments. It is further shown that branched discharge channels can produce models
that correctly follow the channel paths. If images are not accurately normalised
for lens correction and slight camera tilts, missing segments and duplication of
reconstructed branches are evident in the models. Furthermore, it is shown that
the algorithm also fails for image perspectives with angular separations less than
15◦, additional redundant branches are produced in addition to thicker channel
segments.
iv
Acknowledgements
I would like to thank Dr. Ken J. Nixon for his enthusiasm, guidance and constant
mentorship throughout the duration of this work. I would also like to extend my
heartfelt gratitude to Prof. Ian R. Jandrell for providing me with so many great
opportunities. Last but not least, I would like to thank the High Voltage and
Lightning EMC Research Groups and the staff of Genmin Laboratory for their
neverending support and encouragement.
The following organisations are gratefully acknowledged for funding and supporting
the High Voltage and Lightning EMC Research Groups:
• CBI-Electric for direct support and funding the Chair of Lightning at the
University of the Witwatersrand.
• Eskom through the Tertiary Education Support Programme (TESP).
• The National Research Foundation (NRF).
• The Department of Trade and Industry (DTI) for Technology and Human
Resources for Industry Programme (THRIP) funding.
vContents
Declaration i
Abstract iii
Acknowledgements iv
Contents v
List of Figures x
List of Tables xvi
List of Symbols and Notation xvii
Abbreviations xix
Nomenclature xxi
1 Introduction 1
2 Background 4
2.1 The Lightning Discharge . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Cloud-to-Cloud (CC) Lightning . . . . . . . . . . . . . . . . . 6
2.1.2 Ground Lightning Flashes . . . . . . . . . . . . . . . . . . . . 6
2.2 Lightning Photography . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 Challenges of Lightning Photography . . . . . . . . . . . . . . 10
2.2.2 Existing Research: Photography of Lightning . . . . . . . . . 11
2.3 Lightning to Tall Structures . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.1 World-Wide Lightning Research of Tall Structures . . . . . . 13
2.3.2 Towers in Johannesburg, South Africa . . . . . . . . . . . . . 14
2.4 3D Lightning Modelling Methods . . . . . . . . . . . . . . . . . . . . 17
Contents vi
2.4.1 Scientific Lightning Simulation Methods . . . . . . . . . . . . 17
2.4.2 Rendered Applications . . . . . . . . . . . . . . . . . . . . . . 18
2.4.3 Existing Research: 3D Channel Reconstruction . . . . . . . . 19
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3 Approach Taken 22
3.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 System and Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3 Contribution of this Dissertation . . . . . . . . . . . . . . . . . . . . 24
3.3.1 Main Contribution . . . . . . . . . . . . . . . . . . . . . . . . 25
3.3.2 Possible Extension to this Work . . . . . . . . . . . . . . . . 26
4 System Design 27
4.1 System Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2 Photographic Equipment . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2.1 Data Filtering: Optical . . . . . . . . . . . . . . . . . . . . . 28
4.2.2 Cameras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2.3 Camera Operation . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2.4 Camera Safety in Laboratory Environment . . . . . . . . . . 32
4.2.5 Camera Limitations in Functionality . . . . . . . . . . . . . . 33
4.2.6 Network and Communication . . . . . . . . . . . . . . . . . . 36
4.2.7 Data Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3 Data Conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4.3.1 Pre-Processing of Discharge Channel Images . . . . . . . . . 38
4.4 Three-Dimensional Reconstruction Algorithm . . . . . . . . . . . . . 46
4.4.1 Limitations of Model Reconstruction . . . . . . . . . . . . . . 47
4.4.2 Two-Image Reconstruction . . . . . . . . . . . . . . . . . . . 50
4.4.3 Three-Image Reconstruction . . . . . . . . . . . . . . . . . . . 51
4.5 Testing Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5 HV Laboratory Investigation 58
5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.2 Experiment A-1: General Investigation . . . . . . . . . . . . . . . . . 60
5.2.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . 60
5.2.2 Reconstruction Results . . . . . . . . . . . . . . . . . . . . . . 61
5.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Contents vii
5.3 Experiment A-2: Single-Channelled Verification . . . . . . . . . . . . 64
5.3.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . 64
5.3.2 Reconstruction Results . . . . . . . . . . . . . . . . . . . . . . 65
5.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.4 Experiment A-3: Branched-Channel Evaluation . . . . . . . . . . . . 67
5.4.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . 67
5.4.2 Reconstruction: Part 1 . . . . . . . . . . . . . . . . . . . . . . 68
5.4.3 Reconstruction: Part 2 . . . . . . . . . . . . . . . . . . . . . . 69
5.4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6 Physical Lightning Investigation 73
6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.2 Experiment B-1: Single Channel (Tuscon) . . . . . . . . . . . . . . . 74
6.2.1 Experimental and Setup . . . . . . . . . . . . . . . . . . . . . 74
6.2.2 Reconstruction Results . . . . . . . . . . . . . . . . . . . . . . 75
6.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.3 Experiment B-2: Multiple Channels (South Dakota) . . . . . . . . . 77
6.3.1 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . 78
6.3.2 Reconstruction Consideration . . . . . . . . . . . . . . . . . . 80
6.3.3 Reconstruction Results: Part 1 . . . . . . . . . . . . . . . . . 80
6.3.4 Reconstruction Results: Part 2 . . . . . . . . . . . . . . . . . 82
6.3.5 Reconstruction Results: Part 3 . . . . . . . . . . . . . . . . . 83
6.3.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
7 Discussion and Future Work 89
7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
7.2 Single-Channelled Investigation . . . . . . . . . . . . . . . . . . . . . 90
7.2.1 Laboratory Discharges . . . . . . . . . . . . . . . . . . . . . . 90
7.2.2 Lightning Discharges . . . . . . . . . . . . . . . . . . . . . . . 91
7.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7.3 Multiple-Channelled Investigation . . . . . . . . . . . . . . . . . . . 92
7.3.1 Laboratory Discharges . . . . . . . . . . . . . . . . . . . . . . 92
7.3.2 Lightning Discharges . . . . . . . . . . . . . . . . . . . . . . . 93
7.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Contents viii
7.4 System Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
7.4.1 Reconstruction Framework . . . . . . . . . . . . . . . . . . . 94
7.4.2 Image Pre-Processing . . . . . . . . . . . . . . . . . . . . . . 94
7.4.3 Reconstruction Algorithms . . . . . . . . . . . . . . . . . . . 95
7.4.4 Testing Model Accuracy . . . . . . . . . . . . . . . . . . . . . 96
7.4.5 Future Work on Image Data . . . . . . . . . . . . . . . . . . 97
8 Conclusion 100
References 102
A Discharge Channel Photography 106
A.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
A.2 Possible Camera Solutions . . . . . . . . . . . . . . . . . . . . . . . . 106
A.3 Summary of Camera Settings . . . . . . . . . . . . . . . . . . . . . . 107
A.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
B Motivation for Three-Dimensional Study of Lightning 110
B.1 Preamble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
B.2 Paper Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
C Ground-Work for System 117
C.1 Preamble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
C.2 Paper Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
D High Voltage Testing on Large Channel Paths with Discontinuities124
D.1 Preamble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
D.2 Paper Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
E Small-Scale Investigation on Reconstruction with Cameras at Dif-
ferent Elevations 130
E.1 Preamble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
E.2 Paper Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
F Preliminary Testing on One Image Perspective of Lightning 136
F.1 Preamble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
F.2 Paper Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
G Single-channelled Lightning Testing 142
Contents ix
G.1 Preamble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
G.2 Paper Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
xList of Figures
2.1 Cloud to ground (CG) lightning in the same frame as Cloud-to-Cloud
(CC) lightning. (a) In one event, a downward CG lightning strike in
the distance (left) preceeds a CC lightning event along the base of
the clouds, branching towards the camera position. (b) Downward
negative lightning flash as a CG strike (left) with CC activity in the
same frame (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Cloud-to-cloud (CC) lightning. (a) Possible intercloud lightning,
(b) Cloud-to-air lightning. . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Negative downward lightning, the most common type of CG lightning
usually portrayed by downward branching. . . . . . . . . . . . . . . . 8
2.4 Upward lightning on Brixton tower visually characterised by branch-
ing in the upward direction. . . . . . . . . . . . . . . . . . . . . . . . 9
2.5 Brixton (237 m) and Hillbrow towers (270 m tall) are indicated as the
highest points in the Johannesburg skyline to date, laterally separated
by approximately 4.8 km. . . . . . . . . . . . . . . . . . . . . . . . . 14
2.6 Negative downward flashes on Brixton tower, appearing to originate
from overhead the location of the surveillance camera. Flash occur-
ring on (a) 1 January 2011 at 15:44:56.980s (b) 8 February 2011 at
17:56:12.100s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.7 Possible flash to Hillbrow tower photographed from surveillance loca-
tion of the tower. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.8 A basic representation of the reconstruction method. . . . . . . . . . 20
3.1 Time series of a tortuos lightning channel with unknown spatial
distribution taken on 19 December 2010 at 02:52:42−0.930 s. (a) CC
preceeding ground flash (Reference time: +0 s) (b) CG discharge
(+0.100 s) (c) +0.210 s (d) +0.330 s (e) +0.660 s (f) +0.770 s. . . . . 23
3.2 Demonstration of downward negative flashes that appear to be inter-
cepted by upward leaders from the ground. This is demonstrated by
a sharp change of direction in the channel path. . . . . . . . . . . . . 25
List of Figures xi
4.1 Block diagram demonstrating the three-dimensional reconstruction
system overview and flow. . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2 Discharge image acquisition using optical filters and cameras. . . . . 28
4.3 Comparison of lightning images with different optical filter combina-
tions. These images are taken from separate lightning events with the
same camera. (a) No filters (b) Cross-polarised filters. . . . . . . . . 29
4.4 Comparison of high voltage discharge images with different optical
filter combinations. These images are taken from separate lightning
events with the same camera. (a) Cross-polarised filters (b) Cross-
polarised and infrared filters (c) Cross-polarised, infrared and violet
filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.5 Image splicing for Axis 207W. Two subsequently occurring discharges
are captured between a frame change, Marker 1 indicates the bottom
portion of the first flash, and Marker 2 indicates the top portion of
the second flash. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.6 Image splicing and pre-buffer induced corruption of information for
Axis M1344. Images are taken of the same discharge, 94◦ laterally
separated. (a) Vertical image splicing, (b) Vertical image splicing and
pre-buffer corruption. . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.7 Overexposure for Axis 207W with the use of optical filters. (a) Over-
exposed frame (b) Normal frame of overexposed flash 20 ms after (a)
is photographed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.8 Channel reflections recorded on an image taken with the Axis 207W.
The number of the reflections depend on the intensity of the illumi-
nosity, either one or three reflections. Marker 1 indicates the original
channel, Marker 2 indicates the first reflection (more common), Mark-
ers 3 and 4 indicate reflections of 1 and 2, respectively. . . . . . . . . 37
4.9 Channel isolation using image pixel difference comparisons with an
image occurring several frames before the channel is photographed.
Marker 0 indicates the fixed image, Markers 1 − 3 indicate images
identified with significant pixel difference. . . . . . . . . . . . . . . . 40
4.10 Image difference of a lightning event occurring on 8 February 2011
at 18:13:47.900. (a) Original image (b) Difference image with a
mismatch of 40, 063 pixels (of 600× 480 image resolution). . . . . . . 41
4.11 Black and White Boolean filter using threshold values between (0 −
255) implemented for sample images used in Figure 4.10. (a) Thresh-
old value of 70 (b) Threshold value of 100. . . . . . . . . . . . . . . . 42
List of Figures xii
4.12 Smooth Bool process. . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.13 Smooth and Boolean filter iterations (a) Original image with focus
area labelled with Marker 1 (b) First iteration of Smooth filter with
scatter constant set to 5 (c) First iteration with Boolean filter with
threshold at 90 (d) Second iteration of Smooth filter with scatter con-
stant set to 20 (e) Second iteration with Boolean filter with threshold
at 80. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.14 Isolated images amalgamated in a single image to reduce timing issues. 45
4.15 A simple branched channel generated as an example to illustrate
the image placement in the reconstruction environment. (a) Re-
constructed model about environment origin surrounded by images
contributing to its reconstruction (b) Zoomed view illustrating the
stacked nature of the model design. . . . . . . . . . . . . . . . . . . . 47
4.16 Camera 1 — Timing inconsistencies capturing different levels of infor-
mation, in particular, Frame 2 producing branching information not
evident in any other frame of the event. (a) Frame 1, (b) Frame 2,
(c) Frame 3, (d) Frame 4, (e) Frame 5, (f) Frame 6. . . . . . . . . . 48
4.17 Camera 2 — Matching lightning event captured 34◦ from Figure 4.16
at a lower image resolution. (a) Frame 1, (b) Frame 2, (c) Frame 3. . 48
4.18 Basic channel reconstruction algorithm for single-channelled discharges,
resolving channel segments by a series of two-dimensional geometric
problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.19 Redundancies for branched channels from images. (a) Two branches
are assumed as part of the channel, and two are assumed by be
redundant (b) Resolving channel branch redundancies using a third
image. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.20 Algorithm for constructing channel segments from three images to
resolve channel redundancies, using the third image as verification
(a) Construction of C1 using I1 for verification (b) Construction of C2
using I2 for verification (c) Construction of C3 using I3 for verification. 53
4.21 Channel segment constructed from resolved channel segments C1, C2
and C3 from Figure 4.20 if first detect option is true. . . . . . . . . . 54
4.22 Testing procedure comparing pixel mismatching of two images (a) Cir-
cle (represents original Boolean image) (b) Square (represents image
of model at same perspective) (c) Difference between the two images
indicated by white pixels. . . . . . . . . . . . . . . . . . . . . . . . . 56
List of Figures xiii
5.1 Experimental setup for laboratory Experiment A-1 to determine
the optimal camera positions for reconstruction — Current camera
configuration at 45◦. . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.2 Three-camera angular separations for Experiment A-1 (a) Camera
separation of 30◦ (b) Camera separation of 45◦ (c) Camera separation
of 60◦ (d) Camera separation of 120◦, and (e) Camera separation of
90◦. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.3 A set of images samples taken in the high voltage laboratory inves-
tigation with three camera perspectives at eye level (a) Camera 1 at
0◦ (b) Camera 2 at 120◦ (c) Camera 3 at 240◦. . . . . . . . . . . . . 65
5.4 Reconstructed model from Figure 5.3. Input data can be seen behind
the model channel, to match the accuracy of reconstructed channel
path and shape for Cameras 1 and 2. (a) Camera 1 at 0◦ (b) Camera
2 at 120◦ (c) Perspective of reconstructed model at 240◦. . . . . . . . 66
5.5 Verification through comparing third photographed image from Cam-
era 3 at 240◦, not used as an input for the model reconstruction.
(a) Original image (b) Boolean image (c) Reconstructed model at
corresponding angle (background underlay of channel shape of origi-
nal channel, for direct comparison). . . . . . . . . . . . . . . . . . . . 66
5.6 Reconstructed model of branched HV discharge channel using two
input images. In each pair, shows the resulting Boolean image (left),
and corresponding perspective of the reconstructed model (right) (a-
b) Perspective 2 at 45◦ (c-d) Perspective 3 at 90◦. . . . . . . . . . . 68
5.7 Reconstructed model of branched HV discharge channel. In each
pair, shows the resulting Boolean image (left), and corresponding
perspective of the reconstructed model (right) (a-b) Perspective 1
at 0◦ (c-d) Perspective 2 at 45◦ (e-f) Perspective 3 at 90◦. . . . . . . 69
5.8 Image of the two-image reconstructed model at an arbitrary perspec-
tive indicating inaccurage branching definition. (a) Full length with
marked focus (b) Zoomed image of marked focus. . . . . . . . . . . . 70
5.9 Image of the three-image reconstructed model at an arbitrary perspec-
tive indicating duplicated channels per branch and missing segments.
(a) Full length with marked focus (b) Zoomed image of marked focus. 71
6.1 Images taken of a lightning flash in Tuscon USA in 2007 for two dif-
ferent perspectives approximately 34◦ apart. (a) Camera S1 (b) Cam-
era S2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
List of Figures xiv
6.2 Reconstructed model of a single channelled lightning flash. (a) Cam-
era S1: Boolean image (b) Camera S1: Reconstructed image (c) Cam-
era S2: Boolean image (d) Camera S2: Reconstructed image. . . . . 75
6.3 Original image from Camera S1 perspective indicating area of interest
for demonstrating errors in resolution in the reconstructed model. . . 76
6.4 Zoomed in area of interest showing resolution errors on the recon-
structed lightning model from Camera S1 perspective. (a) Original
image (b) Boolean image (c) Corresponding image of reconstructed
model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6.5 Camera W1 perspective of upward lightning leader propagation of a
branched flash photographed at multiple perspectives. (a) Multiple
channels (b) Return stroke. . . . . . . . . . . . . . . . . . . . . . . . 77
6.6 Upward lightning leader propagation of a branched flash photographed
from Camera W2 to Camera W5. (a) Camera W2 (b) Camera W3
(c) Camera W4 (d) Camera W5. . . . . . . . . . . . . . . . . . . . . 78
6.7 Fully branched channel Boolean images of upward flash return stroke;
cropped to include mutually inclusive data of the channel (a) Cam-
era W1 at 0◦ (b) Camera W2 at 12◦ (c) Camera W3 at 15◦. . . . . . 81
6.8 Reconstructed lightning channel of the fully branched channel of the
upward flash return stroke using two images (a) Reconstructed per-
spective of Camera W1 (b) Reconstructed perspective of Camera W2
(c) Reconstructed perspective of Camera W3 (d) Triple duplication
of a channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.9 Two-branched channel Boolean images of upward flash return stroke;
cropped to include mutually inclusive data of the channel (a) Cam-
era W1 at 0◦ (b) Camera W2 at 12◦ (c) Camera W3 at 15◦. . . . . . 82
6.10 Reconstructed lightning channel of the two-branched channel of the
upward flash return stroke using two images (a) Reconstructed per-
spective of Camera W1 (b) Reconstructed perspective of Camera W2
(c) Reconstructed perspective of Camera W3 (d) Extent of the full
model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.11 Single branched channel Boolean images of upward flash return stroke;
cropped to include mutually inclusive data of the channel (a) Cam-
era W1 at 0◦ (b) Camera W2 at 12◦ (c) Camera W3 at 15◦. . . . . . 84
6.12 Reconstructed lightning channel of the single branched channel of the
upward flash return stroke using two images (a) Reconstructed per-
spective of Camera W1 (b) Reconstructed perspective of Camera W3. 84
List of Figures xv
6.13 Reconstructed lightning channel of the single branched channel of the
upward flash return stroke using three images (a) Reconstructed per-
spective of Camera W1 (b) Reconstructed perspective of Camera W2
(c) Reconstructed perspective of Camera W3. . . . . . . . . . . . . . 85
6.14 Channel thickness distortion modelled in the reconstruction due to
acute angles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
6.15 Verification process for redundant channels at acute angles. (a) Iden-
tification of cylinder centers and respective points (marked with ’x’)
to calculate radii (b) Virtual cylinders with radii determined by the
averaged distances of ‘x’ points (c) Third image verification incor-
rectly identifying all cylinders as valid. . . . . . . . . . . . . . . . . . 87
7.1 Camera views on Brixton tower indicating an approximate 70◦ sepa-
ration between the two sites. . . . . . . . . . . . . . . . . . . . . . . 98
7.2 Two camera sites providing vastly different camera elevations observ-
ing Brixton tower. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
xvi
List of Tables
4.1 Camera safety capabilities for operation in either the high voltage
laboratory or phyical lightning investigations. . . . . . . . . . . . . . 32
4.2 Image processing filters using basic implementation of existing VTK
classes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.3 Three-image reconstruction algorithm steps to reconstructing channel
segments for first detect option. . . . . . . . . . . . . . . . . . . . . . 53
4.4 All seven algorithm options available for individual reconstruction
cases for two or three image reconstructions. . . . . . . . . . . . . . . 55
5.1 Visual evaluation of all laboratory datasets providing number of re-
constructed images containing the listed characteristics. . . . . . . . 63
5.2 Reconstruction configurations for branched HV discharge channel
evaluation using two- and three-image algorithms. . . . . . . . . . . 68
6.1 Geographic information of cameras in relation to a flash photographed
on a tower in South Dakota. . . . . . . . . . . . . . . . . . . . . . . . 79
6.2 Configurations for cameras participating in the photography of the
flash occurring on the South Dakota tower. . . . . . . . . . . . . . . 79
7.1 Summary of all experiments performed for reconstruction of discharge
channels under various algorithm configurations. . . . . . . . . . . . 90
7.2 Geographic information for Brixton tower and the relative camera
locations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
A.1 General camera settings configured for the laboratory and/or physical
investigation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
xvii
List of Symbols and Notation
Physical Quantities
Ad Collection area of isolated structure, m2
Cd Factor taken into account for location of structure
Heff Effective height
Hs Height of tall structure, m
ND Annual number of downward flashes to a structure, flashes/year
NF Annual number of flashes to a structure (all flashes), flashes/year
Ng Lightning ground flash density, flashes/km2/year
Pu Upward probability of flashes to a structure
R Gap geometry and spacing (nature and dimensions of ground elec-
trodes), m
Re Effective radius, m
Req Equivalent radius, m
Td Annual number of thunderstorm days, days
Ulc Continuous leader inception voltage potential, kV
Software Quantities
εpm Pixel mismatch error, pixels
Epm Percentage mismatched pixel error, %
Ih Height of image, pixels
In(center) Center normal of an 1-pixel high white band from an image, where n
denotes image number, pixels
In(left) Outer left normal of an 1-pixel high white band from an image, where
n denotes image number, pixels
In(right) Outer right normal of an 1-pixel high white band from an image, where
n denotes image number, pixels
Iw Width of image, pixels
List of Symbols and Notation xviii
r1 Radial distance from segment center to normal I1(center) intersection
with normal I2(right), pixels
r2 Radial distance from segment center to normal I1(center) intersection
with normal I2(left), pixels
r3 Radial distance from segment center to normal I2(center) intersection
with normal I1(right), pixels
r4 Radial distance from segment center to normal I2(center) intersection
with normal I1(left), pixels
Rcs Radius of a 1-pixel high channel segment, pixels
xix
Abbreviations
2D two-dimensional
3D three-dimensional
C++ Cplusplus
CC Cloud-to-Cloud
CG Cloud-to-Ground
CN Canadian National
CSIR Council for Scientific and Industrial Research
DUT Device Under Test
fps frames per second
FTP File Transfer Protocol
HV High Voltage
IC Intra-Cloud
IP Internet Protocol
JPEG Joint Photographic Experts Group - Image file format
LAN Local Area Network
LDN Lightning Detection Network
Abbreviations xx
MKV Matroska video
RAM Random Access Memory
SALDN South African Lightning Detection Network
SD Secure Disk
VTK Visualisation Tool-Kit
xxi
Nomenclature
Boolean image An image of black and white pixels, where a white
pixel (colour value: 255) is regarded as a TRUE
representation of discharge channel information, and a
black pixel (colour value: 0), a FALSE representation,
therefore containing redundant information.
Filter Terminology used by VTK for a process that accepts
inputs, makes necessary changes according to func-
tionality, and produces an output with changes.
Final jump The intersection between the downward stepped
leader and the connecting upward leader, which deter-
mines the striking or termination point of the lightning
flash.
Model A schematic description of a system, theory, or phe-
nomenon that accounts for its known or inferred
properties and may be used for further study of its
characteristics. — TheFreeDictionary.com
Modelling verb of model.
Negative discharge A discharge initiated by a negative leader, indepen-
dent of direction of leader propagation, (classical
definition).
Positive discharge A discharge initiated by a positive leader, independent
of direction of leader propagation, (classical defini-
tion).
Nomenclature xxii
Reconstructing verb of reconstruction.
Reconstruction (Reconstruct) To re-create in the mind from given or
available information. — Dictionary.com
Return stroke A surge of electrical current travelling back through
the channel defined by the leader paths.
Simulation The representation of the behaviour or characteristics
of one system through the use of another, esp. a
computer program designed for the purpose. —
Dictionary.com
Striking distance The height of a downward leader tip above ground at
which an upward connecting leader is initiated.
1Chapter 1
Introduction
Lightning models form a large basis of research into further investigating the physical
construction and progression of the meteorological phenomenon [1]. These models
have a significance into understanding the nature of discharge channels through
the examination of the shape, tortuosity, span, factors affecting its formation, risk
involved with Cloud-to-Ground (CG) events and provides a scope for minimising
such dangers. The software simulation of lightning channels have become a necessity
for analysing an otherwise fast, intangible and non-repeatable event. This study
provides a investigation into the feasibility of reconstructing lightning discharge
channels, which is compared with data produced from High Voltage (HV) laboratory
investigations. Multiple digital images photographed of discharges are used as the
fundamental datasets in conjunction to camera positions relative to the discharge
locations. These reconstructed discharge channel models are examined within a
three-dimensional (3D) virtual environment to visualise the channel using pan, tilt
and zoom user capabilities.
A system is designed to capture two-dimensional (2D) images of a discharge channel
and represent the discharge as a 3D model within a 3D interactive environment. Two
key investigations are conducted in the form of small-scale HV laboratory and large-
scale physical lightning experiments. The investigations provide two fundamental
channel shapes involved with discharge channels: single-channelled and multiple-
channelled discharges. The use of image data on each of these shapes will provide
verfication on the algorithms used to reconstruct the channels. The results from
these investigations are compared to determine the feasibility of reconstructing
lightning discharge channel models using digital images.
Chapter 2 discusses the background information associated with lightning, the
Chapter 1 — Introduction 2
photography of lightning, lightning modelling methods and 3D modelling methods.
A review on existing research associated with this work is also identified.
Chapter 3 evaluates the approach taken on the proposed solution to determining
the feasibility of reconstructing a 3D model of a lightning discharge channel. The
assumptions and constraints are presented to determine the necessary approach
concerning the problem statement. The motivation behind the undertaking of this
research is provided with its significance in the field of lightning research.
Chapter 4 provides an overview on the system design . The system is discussed
from its photography of discharge channels, to the production of the reconstructed
model. A discussion of the photographic equipment used for the investigations is
provided, including the operations and limitations involved. Data conditioning of
the images is discussed to isolate discharge channel information in each frame, and
prepare Boolean images as inputs into the modelling framework. Reconstruction
algorithms are discussed for the reconstructing both single- and multiple-channelled
discharges. The testing methodology in determining the accuracy of reconstructed
models is also discussed.
Chapter 5 investigates the reconstruction of discharges in a small scale HV labo-
ratory environment. This investigation allows for the controlled simulation of the
camera positioning which can be compared to the physical scenario with regards to
natural lightning. Several tests are performed to evaluate the performance of the
algorithm configurations and provide verification of reconstructing single-channeled
and multiple-channelled discharges.
Chapter 6 investigates the reconstruction of natural lightning discharges in the large,
uncontrolled, physical lightning environment using a limited set of photographed
images. Single-channelled and multiple-channelled discharge channels are recon-
structed.
Chapter 7 summarises the results of the laboratory and physical investigations.
A discussion of the project feasibility and the future work of reconstructing
single-channelled and multiple-channelled discharges and an evaluation of the system
is provided. All results are provided with respect to the reconstruction system
discussed in Chapter 4.
Chapter 8 discusses the final findings of the system and its investigation scenarios
and provides a conclusion to the work.
Chapter 1 — Introduction 3
Appendix A summarises additional information on cameras and camera options for
the photography of discharge channels.
Appendix B presents a paper published and presented at a peer-review conference,
to provide a background and motivation for this research investigation.
Appendix C presents a paper published and presented at a peer-review conference,
to provide ground work on the system and preliminary testing performed in the HV
laboratory.
Appendix D presents a paper published and presented at a peer-review conference,
providing an investigation into larger discontinuous laboratory gaps.
Appendix E presents a paper published and presented at a peer-review conference, to
provide preliminary laboratory work into investigating reconstructions of discharges
if cameras are placed at different elevations.
Appendix F presents a paper published and presented at a peer-review conference,
providing confidence in reconstructing branched lightning discharge channels with
no 3D definition.
Appendix G presents a paper published and presented at a peer-review conference,
producing a reconstruction of single-channelled lightning discharge.
4Chapter 2
Background
Lightning research started with ground-level observations [2]. These fast, almost
instantaneous events (durations of µs) are typically recorded in a two-dimensional
(2D) capacity. With the development of camera technology, more information
has been resolved through faster camera framerates and monitoring techniques.
Simulated lightning models take it a step further to understand its statistical nature.
Through the advancement of computer technology, new exciting ways to represent
the lightning event have been made possible, whether for research or entertainment
media purposes. By combining the two technologies, the possibility for recon-
structing three-dimensional (3D) lightning discharge channels using photographs of
a lightning event can be achieved.
Existing research which provides insight into the development of this work is sum-
marised in four parts. Firstly, the lightning phenomenon is discussed and classified.
Secondly, the photography of the fast transient discharge events is defined. Then,
research relating to lightning attachment to or extending from tall structures is
discussed and two towers in Johannesburg are introduced and evaluated. Finally,
several different ways of representing lightning by means of models are discussed,
which leads to the options available for 3D modelling methods. In particular, a 3D
reconstruction method for modelling High Voltage (HV) discharge channels that was
developed in 2008 is briefly discussed [3]. This study extends the real application to
lightning discharge channels using the same system basis developed in 2008. A full
discussion of the system is presented with additional adjustments.
Section 2.1 provides a brief discussion on the lightning discharge is presented to
cover the lightning terminology that is used in this document.
Section 2.2 discusses the challenges of lightning photography ; this includes an
Chapter 2 — Background 5
overview of current solutions and a discussion of possible camera solutions for this
work.
Section 2.3 investigates the interaction between lightning and tall structures.
This is conducted by introducing some notable ground-work on this topic by Eriksson
in 1978 [4], and then identifying tall structures around the world that are currently
platforms for lightning research. Two tall towers in Johannesburg, South Africa are
introduced: Brixton tower and Hillbrow tower.
Section 2.4 discusses the existing three-dimensional modelling methods for
lightning. The simulation of lightning is not new or uncommon. However, the
reconstruction of lightning discharge channels of known, photographically recorded
events is a relatively new topic and not extensively documented. Therefore, ex-
isting methods that closely resemble the basis of this study are reviewed and the
reconstruction of lightning or HV channels is discussed in the existing research.
2.1 The Lightning Discharge
(a) (b)
Figure 2.1: Cloud to ground (CG) lightning in the same frame as Cloud-to-Cloud
(CC) lightning. (a) In one event, a downward CG lightning strike in the distance
(left) preceeds a CC lightning event along the base of the clouds, branching towards
the camera position. (b) Downward negative lightning flash as a CG strike (left)
with CC activity in the same frame (right).
This section introduces simple terms that relate to the lightning discharge, which is
addressed in the rest of this document. In Figure 2.1, a sample of the two common
types of lightning are demonstrated, the downward negative Cloud-to-Ground (CG)
Chapter 2 — Background 6
lightning strike, and Cloud-to-Cloud (CC) lightning. Each of these lightning types
are discussed in more detail.
Lightning Nomenclature
In different contexts, there are several defining nomenclature for lightning termi-
nology that is used. This document refers to classical definitions of lightning
terminology; in particular ‘negative discharge’ and ‘positive discharge’ is defined
below:
Negative discharge: A discharge that is initiated by a negative leader,
independent of direction of leader propagation.
Positive discharge: A discharge that is initiated by a positive leader,
independent of direction of leader propagation.
2.1.1 Cloud-to-Cloud (CC) Lightning
The more commonly occurring type of lightning is referred to as Cloud-to-Cloud
(CC) or Intra-Cloud (IC) lightning. Two examples of these types of lightning
discharges are illustrated in Figure 2.2. This is a blanket-term for the following
types of discharges [1]:
• Intracloud (from one charge center to another charge center in the same cloud),
• Intercloud (from one charge center in a cloud to another charge center in a
different cloud) and,
• Cloud-to-air discharges (from a charge center in a cloud to a charge pocket in
the air).
2.1.2 Ground Lightning Flashes
The ground flash is the type of lightning discharge that engineers in the lightning
field of research are mostly concerned about, and is commonly termed the Cloud-to-
Ground (CG) for downward discharges, and ground-to-cloud for upward discharges.
Chapter 2 — Background 7
(a) (b)
Figure 2.2: Cloud-to-cloud (CC) lightning. (a) Possible intercloud lightning,
(b) Cloud-to-air lightning.
Lightning ground discharges are initiated by charge separation in a cumulonimbus
cloud, forming a charge center in the cloud [1, 5]. From this charge center, a charge
column or stepped leader is created, comprised of positive or negative charge carriers.
The stepped leader is a self-sustaining process and can also split into branches that
propagate towards the ground, depending on the leader polarity. The electric field
is increased on the ground due to the approaching stepped leaders. Therefore,
upward connecting leaders are initiated from higher points on the ground of the
opposite polarity that travel upwards to meet with the approaching downward
stepped leader. The intersection between the downward stepped leader and the
connecting leader, also called the final jump, determines the striking or termination
point of the lightning flash. The point of intersection from the ground termination
location is called the striking distance. At the point of intersection, a return stroke
travels up the channel back to the cloud. The return stroke illuminates the channel
such that the naked eye can observe the lightning event, and is usually synonomous
with CG lightning.
A large majority of ground flashes contain several strokes, where subsequent strokes
occur due to the remaining charge in the charge center of the cloud travels down the
path of the initial return stroke channel, causing the flickering visual characteristic
of lightning. A lightning flash can be made up of multiple strokes with the same, or
sometimes unique termination points.
Chapter 2 — Background 8
(a) (b)
Figure 2.3: Negative downward lightning, the most common type of CG lightning
usually portrayed by downward branching.
Downward Negative CG Lightning
The most common type of CG lightning flash is a downward negative discharge,
believed to account for approximately 90% of all CG flashes [1]. Negative downward
lightning is visually characterised by the appearance of multiple downward branching
in the channel propagation towards the ground, as demonstrated in Figure 2.3.
This type of lightning discharge is initiated by the generation of negative charge
centers near the bottom of the cloud [1, 5]. From this charge center, a negatively
charged stepped leader is created and often splits into branches that propagate
towards the ground.
Downward Positive CG Lightning
Positive CG discharges are less common than its negative counterpart, and is
believed to account for approximately 10% of all CG flashes [1]. Early studies of this
lightning type produced some confusion and misclassification. However, attention
was brought to continued research of positive flashes due to several characteristic
properties, which includes high recorded currents, being the dominant type in cold
seasons (most notable in Japanese winter storms). Visual characteristics of positive
CG flashes include:
1. Mostly single strokes (per flash)
2. Long continuing currents (tens to hundreds of milliseconds)
Chapter 2 — Background 9
3. Return stroke preceeded by cloud activity
4. Long horizontal channels (tens of kilometers)
These positive CG flashes have been reported to occur at the beginning or towards
the end of a thunderstorm, once most of the negative charge has been depleted from
the clouds [1]. It is believed that the flashes are initiated in the upper positive region
of the thundercloud, although there is also evidence of long horizontal discharges
initiated from other layers (such as the layer near the 0◦ isotherm).
Upward Lightning
(a) (b)
Figure 2.4: Upward lightning on Brixton tower visually characterised by branching
in the upward direction.
Upward lightning mostly propagates from points on the ground which produce a
concentrated electric field [1, 4]. The field is often enhanced by higher ground or
structure geometries with relative heights of approximately 100m. Higher objects
tend to produce a higher probability of initiating upward discharges. Upward
lightning is visually characterised by the appearance of upward branching in the
channel propagation, as demonstrated in Figure 2.4. Upward lightning can also be
classified by polarity; the classical definition defining the polarity according to the
initiating leader from the ground, and the newer definition defined by Rakov and
Uman defines the polarity according to the charge lowered to the ground [1]. This
document uses the classical definition of lightning polarity.
Chapter 2 — Background 10
2.2 Lightning Photography
Early observations of lightning started with open-aperture photography. Lightning
is only visible within several microseconds and each flash takes on a unique channel
path. Despite these challenges, lightning photography has helped to immortalise
lightning flashes and assisted researchers to identify common characteristics of the
different types of lightning. Further information is provided in Appendix A.
Hoffert and Walter obtained the first useful photographs around 1889 − 1902 that
showed the seperate strokes of a lightning flash [2]. This was achieved by manually
rocking an ordinary camera on a set axis with an open lens exposure. Due to
this manual nature, the time intervals between strokes could not be accurately
determined. Later, the Boys camera played an important role into providing some
additional understanding in the temporal nature the lightning strokes and subse-
quent strokes, measuring of time intervals between strokes to a few microseconds.
With the advancement of technology, high speed cameras with aperture speeds
ranging to 50, 000 frames per second (fps) or more, have provided opportunities
to observe phenomena surrounding lightning flashes that have yet to be discovered.
Despite the development of cameras reaching speeds of approximately 700, 000 fps,
the camera framerates are limited by the image resolution. As speeds get higher,
image resolutions are subsequently traded off.
2.2.1 Challenges of Lightning Photography
To reconstruct a lightning discharge channel, photographs of an actual lightning
flash event must be captured. The difficulties involved with capturing images of
a lightning flash are listed below. Some of these difficulties also apply to the
photography of general HV channels.
• Event duration
• Intensity of the light discharged
• Unpredictability (or statistical nature) of the event occurrence
• Lack of verification methods
Chapter 2 — Background 11
The short duration of the discharge event presents a difficulty with conventional
photography techniques, and requires a specific choice in the image capture device
or specialised techniques. The intensity of the light emitted from the event may
need to be considered to more photosensitive devices; this varies with the camera
placement from the targetted event. The unpredictability of the event refers to two
specific factors: its position and its time of appearance. This makes the photography
of lightning flashes a statistical problem. From a research point of view, in order to
reconstruct an object, verification needs to be performed with the original object.
This becomes an issue with a lightning or HV discharge channel, due to its unique
discharge path.
For the scope of this work, the use of multiple camera perspectives is essential
in capturing the same discharge channel. Several difficulties arise with a multiple
camera system, which include the synchronisation of the camera devices and the
triggering mechanisms involved, suitable placement of cameras around a known
lightning attachment region and accompanying permission for access, and varying
distances and elevations of camera locations.
2.2.2 Existing Research: Photography of Lightning
There are several researchers that make use photography of lightning, and often
lightning occurring at tall structures. These researchers investigate lightning dis-
charge attachments to tall structures using 2D digital images from conventional
video cameras, or high-speed cameras. These studies provide valuable insight into
the photography of lightning discharges in relation to physical current measurements
taken at the instrumented tower. No mention of a 3D model is included in these
papers, although some produce images from multiple capture devices to provide
a sense of spatial distribution. Additional discussion on lightning photography is
covered in Section 2.3.1.
In 1978, Eriksson examined lightning flashes to a 60-m tall mast using two cameras
spaced approximately 90◦ apart [4]. Eriksson’s investigation is discussed in more
detail in Section 2.4.3.
In 2008, Cummins et al provided some preliminary experimental results that could
ultimately lead to producing a time-resolved 3D model of CG lightning discharges [6].
The paper describes an experimental design, equipment used, and experimental
logistics for photographing lightning discharges from different perspectives, citing
Chapter 2 — Background 12
the challenges in ensuring synchronised camera operation of different perspectives
at remote sites. The preliminary results provide 2D time-resolved images of negative
and positive flashes, and recoil leaders.
In 2008, Saba et al produced research on lesser-documented characteristics of positive
leader using high-speed video photography [7]. A combination of high-speed cameras
were used in conjunction with Lightning Detection Network (LDN) data for analysis
of storms in Brazil and USA.
2.3 Lightning to Tall Structures
Lightning study observations of frequently struck structures have formed an impor-
tant component of lightning research [4, 8, 9, 10]. Since lightning has a tendency
to terminate to (or initiate from) the tallest object in its immediate area — these
structures are typically tall or isolated. It has also been found that structures taller
than 60 meters have the ability to initiate upward lightning [4]; the higher and more
slender the structure, the higher the probability of initiating upward lightning.
In 1978, Eriksson devised equations to determine the lightning incidence to towers;
these equations are still largely being used in the present day [4]. The set of emperical
equations defined the following:
1. An effective height of a structure taking into account the slenderness ratio;
2. The total structure incidence given the ground flash density and the height of
the structure; and
3. A probability based calculation for upward vs downward flashes from/to the
structure.
Eriksson’s equation in Equation 2.1 provides the expected incidence of the tall
structurem, given the effective height of the structure, Heff in m and the ground
flash density of the surrounding area, Ng in flashes/km2/year [11]. Additionally,
Eriksson and Meal’s equation in Equation 2.2 determines the percentage of upward
incidence to a tall structure [12], where Pu is the percentage of upward incidence,
and Hs is the height of the structure in m.
Chapter 2 — Background 13
N = 24× 10−6 ×H2.05s ×Ng (2.1)
where
N = Lightning incidence, flashes
Hs = Height of structure in m (or Heff )
Ng = Ground flash density, flashes/km2/year
Pu = 52.8ln(Hs)− 250 78 < Hs < 518 (2.2)
where
Pu = Upward probability of flashes to a structure, %
Hs = Height of structure (or Heff ), m
2.3.1 World-Wide Lightning Research of Tall Structures
Many tall towers, wind turbines and chimneys have been under observation for
studying lightning and its characteristics. Notable tall structures include:
• Canadian National (CN) tower in Toronto (553 m tall) [1, 8, 13, 14, 15],
• Peissenburg tower in Munich (160 m tall on 288 m high mountainous ter-
rain) [1],
• Gaisberg tower in Salzburg (100 m tall +1287 m above sea level) [1]
• Council for Scientific and Industrial Research (CSIR) mast in South Africa
(60 m) [4],
• Ten-tower configuration in South Dakota (various heights) [16, 17] and
• Fukui Chimney in Japan [18].
CN tower, Peissenburg tower and Gaisburg tower have the advantage of being the
tallest object in the immediate area. Since these towers (or their effective heights)
are so tall, they have a high probability of triggering upward lightning and tower
tips are often situated too high up for optical recordings due to cloud cover or mist.
Chapter 2 — Background 14
These towers are therefore limited in their observed lightning types and photographic
observations to upward flashes. Each of these towers measure lightning on the tower
tips by means of Rogowski coils and electromagnetic sensors.
The CSIR mast was designed to attached downward lightning flashes to its tip and
as of present day, has been decommisioned. Although, an example of a site with a
wider range of lightning observations is in Rapid City, South Dakota, USA, which
consists of ten towers with heights ranging from 91 m to 191 m situated on a ridge
approximately 180 m above the surrounding terrain [16, 17]. This site observes both
upward and downward lightning using a combination of high speed, normal speed
(60 fps) and still cameras, and electromagnetic field sensors.
2.3.2 Towers in Johannesburg, South Africa
Johannesburg is a city in South Africa, situated in the southern hemisphere with a
high ground flash density region of approximately 7.5 – 12 flashes/km2/year [19, 20].
By considering the Johannesburg skyline in Figure 2.5 and with the high ground flash
density in mind, two towers are identified as good candidates to observe lightning
attachment: Brixton tower and Hillbrow tower. Both towers have been historically
common subjects for lightning research in Johannesburg [9, 21].
Brixton Tower
Brixton tower is commercially known as Sentech tower, and formally known as
Hertzog tower [21]. Its construction was completed in 1962. It is approximately
237 m tall and stands quite prominently as the tallest structure in the immediate
2 km radius area.
The expected lightning incidence to the tower is found to be 23.72 flashes/year,
Figure 2.5: Brixton (237 m) and Hillbrow towers (270 m tall) are indicated as
the highest points in the Johannesburg skyline to date, laterally separated by
approximately 4.8 km.
Chapter 2 — Background 15
using Eriksson’s equation in Equation 2.1. Given the height of the tower, Eriksson
and Meal’s equation in Equation 2.2 determines a 61.53% probability of triggering
upward lightning. This means there is an approximate 40% probability of downward
lightning leaders being intercepted by upward propagating leaders initiated from the
tower. This is a much higher probability than most of the world-wide structures
mentioned in Section 2.3.1. Therefore, Brixton tower has a larger variety of upward
flashes and downward lightning interception occurring at its tip.
(a) (b)
Figure 2.6: Negative downward flashes on Brixton tower, appearing to originate
from overhead the location of the surveillance camera. Flash occurring on (a) 1
January 2011 at 15:44:56.980s (b) 8 February 2011 at 17:56:12.100s.
In 1969, Malan observed lightning activity flashing to the tower; noting some strange
thunderstorm behaviour around the tower [21]. The extracts have been taken from
the paper as a reference:
It came as a surprise to find that the 770 ft Hertzog Tower is practically
never struck by lightning when an active thunderstorm passes overhead.
...
Very rarely one of the 2 km distant flashes to ground has been observed
to produce a long horizontal branch which ends on the Tower.
– D.J. Malan (1969) [21]
Similar ‘long horizontal branch(es)’ ending on Brixton tower have been observed in
the onset of this study. Such long horizontal channels, specific to downward negative
lightning attaching to the tower, appear to originate in a cloud charge center located
overhead the building housing one of the surveillance cameras, located approximately
Chapter 2 — Background 16
2 km from the tower. Sample images of such cases illustrating the discharges channels
terminating on the tip of Brixton tower is shown in Figure 2.6.
Appendix B presents a recent study on lightning observed with relation to Brixton
tower, which also serves as a motivation for studying lightning in 3D [22]. This
paper attempts to determine the position of a lightning strike with an unknown
termination point. A ‘third’ dimension is obtained using matched LDN data.
Hillbrow Tower
Hillbrow tower was previously known as the JG Strijdom Tower, named after a
former South African prime minister [23]. Hillbrow tower is 270 m tall, which
makes it one of the highest human made structures in Africa. Its construction
was completed in April 1971. It is located approximately 4.8 km east of Brixton
tower. In Figure 2.7, a possible lightning flash to Hillbrow tower is presented, where
the tower tip is concealed by the tree top.
Figure 2.7: Possible flash to Hillbrow tower photographed from surveillance location
of the tower.
Chapter 2 — Background 17
2.4 3D Lightning Modelling Methods
The concept of three-dimensional modelling is not conventionally associated with
the reconstruction of lightning discharge channels. Although this topic is primarily
based on the reconstruction of 3D models, a broad overview of lightning modelling is
presented. This overview includes the scientific simulation of lightning, in its various
applications, and graphic simulation of lightning in digital media.
Existing research directly related to this research topic is discussed more exten-
sively. These works include the computational reconstruction of lightning or HV
discharge channels using discharge channel information from photographed images.
A complete overview of these solutions is provided, from theoretical studies to
reconstruction of actual discharge events.
Definitions
The term ‘modelling’ is understood as a term used when a physical quantity is
represented in a different medium; in the modern day, usually consisting of com-
puter based representation. In this document, the terms ‘model’, ‘simulation’, and
‘reconstruction’ are used with the following definitions in mind:
Model: A schematic description of a system, theory, or phe-
nomenon that accounts for its known or inferred prop-
erties and may be used for further study of its character-
istics. — TheFreeDictionary.com
Simulation: The representation of the behaviour or characteristics of
one system through the use of another, esp. a computer
program designed for the purpose. — Dictionary.com
Reconstruction
(or Reconstruct):
To re-create in the mind from given or available informa-
tion. — Dictionary.com
2.4.1 Scientific Lightning Simulation Methods
In the scientific field of lightning research, CG lightning leader propagation is most
simply simulated by a straight downward propagating leader [24]. This kind of
Chapter 2 — Background 18
assumption is usually based from research involving the final jump and striking
distances – in the case of a downward negative leader connecting to a positive upward
leader. Similar assumptions are made in the study of the effects of the return
stroke [25]. This simplified representation of a straight downward propagating leader
is, of course, not the case for natural lightning, but has its merits in the study of
fundamental processes.
In 1990, the notable lightning leader propagation simulation was developed by
Dellera and Garbagnati [26, 27]. This research provided insight into the statistical
nature of simulated lightning paths.
In 2009, Gulya´s and Szendenik presented a preliminary mixed physical-probabilistic
3D model to simulate downward negative lightning in relation to ground topogra-
phy [28]. The purpose of this solution is, as discussed by the authors, to simulate
the likely lightning termination points in a given ground topography and provide a
performance evaluation of simulated lightning protection on affected areas. This
computer simulation tool is based on a 2D solution, which combines concepts
based on physical and probabilistic lightning simulation modelling methods. The
development of the proposed 3D simulation model is intended to provide a more
realistic scenario of the ground geometry (i.e. spatial distribution of buildings), and
the resulting lightning termination points of the CG downward strikes.
2.4.2 Rendered Applications
Lightning simulations have mostly been rendered for visual purposes. This includes
digital art, video media (animation) and gaming. The simulation of 3D lightning is
mostly used within the gaming industry. Several solutions to simulating a lightning
channel have been accomplished within the computational application of visualising
lightning channels.
In 1994, Reed and Wyvill were the first to visually simulate lightning using con-
ventional ray-tracing techniques in the computer graphics field [29]. Their method
referred to Dellera and Garbagnati’s paper on scientifically simulating the light-
ning stroke leader progression, by means of probabilistically determining the leader
progression using particle systems [26, 27]. Their simulation was used to render a
realistic looking lightning model for animation purposes, so their solution included
background scenery and using the model as a light source to provide a glowing effect
on nearby objects.
Chapter 2 — Background 19
In 2001, Dobashi et al used Reed and Wyvill’s lightning simulation method to
determine the scattering effect of the lightning light source on surrounding clouds
and atmospheric particles [30].
These solutions have one major flaw; there is no deterministic way of knowing what
lightning actually looks like. By using Dellera and Garbagnati’s lightning simulation
method, these computational solutions only simulate theoretical lightning, which is
what many people have come to believe is the physical appearance of lightning. This
research seeks to reconstruct lightning channels from actual events, as opposed to
merely simulating the phenomenon using probabilistic methods.
2.4.3 Existing Research: 3D Channel Reconstruction
This section reviews the past published methods that have been used to reconstruct
the channel shape of the lightning flash, or HV discharge channels for various
different applications. These methods include a brief description of the environment
in which the discharge channel was photographed, the camera considerations and
subsequent geometries, and the reconstruction methods.
These works provide more relevant background information to reconstruction mod-
elling applications, as most other lightning modelling techniques (determined in
Section 2.4) consider a set of emperical equations and computationally determine a
theoretical propagation path of the lightning channel.
Eriksson’s Three-Dimensional Lightning Reconstruction
In 1979, Eriksson investigated the striking distances of downward negative discharges
striking the CSIR mast in Pretoria, South Africa using a 3D analysis of lightning
photographs [31]. This methodology is described in further detail in this section.
Two image perspectives were obtained at an angular separation of 109◦ for seven
flashes. Cameras were placed facing up towards the mast tip at different inclined
angles (depending on distance from mast and location of the camera), such that
corrections needed to be made through geometrical anyalsis. These corrections were
performed by a computer tool (termed Flash), which was developed by the National
Research Institute for Mathematical Sciences. Both cameras were fitted with a
Chapter 2 — Background 20
graticule grid in front of the lens which provided a scaling measurement with respect
to the focal point of the camera.
The lightning channel information from the images was extrapolated to a 2D Carte-
sian plane, transformed and superimposed onto a (y-z)-x Cartesian plane where the
y and z axis extends upwards in the same direction and the origin is defined as the
mast tip. This transformation was also performed by Flash.
Eriksson defines an overall error in the reconstruction procedure of 3%, citing that
the main errors are determined by input errors and the digitisation process of the
images. Of the seven flashes recorded by the two cameras, only three were classified
as downward negative, and were therefore candidates for reconstruction to determine
striking distances.
Liu and Rapson’s Reconstruction Method
In 2009, Liu and Rapson established a preliminary system to produce a 3D model of
a discharge channel in a controlled laboratory environment [3]. This paper reference
has been provided in Appendix C, but the method is discussed briefly in this section.
It should be noted that this method is the basis of the reconstruction method used
in this study.
Multiple digital images were taken using three surveillance cameras of a discharge
channel from a large HV air-insulated rod-rod gap within a laboratory. The images
were filtered and processed to render a 3D model of the discharge channel using an
application built from open-source software for cross-platform capabilities.
y
x
z
(a) (b)
Figure 2.8: A basic representation of the reconstruction method.
Chapter 2 — Background 21
Figure 2.8 illustrates a simplified representation of functionality of the algorithm [3].
The reconstruction method was based on recreating the laboratory scenario in a
virtual environment, as shown in Figure 2.8a. The 3D problem is reduced to a series
of 2D geometric calculations, by extending normals from the image to the center,
and creating a pixel-high cylinder where the normals meet, as shown in Figure 2.8b.
Gu et al’s Reconstruction Method
In 2011, Gu et al devised a method to reconstruct a long air discharge channel to
study the tortuosity of the channel [32]. A 2-meter long positive switching impulse
gap was investigated in the study. A set of geometric equations were presented
which infer the three-dimensional information of images taken from two orthoganally
placed cameras that have been normalised to boolean images, and channel height.
2.5 Conclusion
This chapter has described four parts that pertain to the foundation of this work: the
lightning discharge; the photography of lightning, lightning research to tall structures
and general 3D modelling and reconstruction methods in representing the lightning
discharge.
The following chapter defines the problem statement to this work. The approach
taken to accomplish this work is outlined through a discussion of the system de-
signed to produce 3D recnstructions of discharge channels and methods used for its
evaluation.
22
Chapter 3
Approach Taken
An overview of the work addressed in this study is discussed in this
chapter, providing the problem statement, the methodology, and the con-
tribution of this work. The methodology used to perform the feasibility
study is provided in the context of the system designed to reconstruct
three-dimensional (3D) discharge channel reconstructions, and the test
data used to perform an evaluation of the system performance.
3.1 Problem Statement
Despite advances in lightning research, there are still many questions left unanswered
about the topic of lightning. It is well known that lightning often takes on very
unique channel shapes, as illustrated in Figure 3.1. It is often very difficult to per-
ceive the channel shape and path with a naked eye or even with the use of expensive
camera equipment without the third spatial dimension. With multiple perspectives
of a specific lightning flash, it is still difficult to perceive its 3D characteristics if no
processing steps are undertaken to represent the channel in three dimensions.
Therefore, the digital reconstruction of a 3D model would provide researchers with
an additional dimension with which to analyse lightning flashes. By obtaining a
3D representation of a discharge channel (lightning or high voltage discharge) the
channel can be properly analysed in an interactive 3D visualised space, with options
to zoom, tilt and pan.
A system is designed to photograph multiple two-dimensional (2D) images of a
discharge channel from different spatial perspectives and represent the discharge as
Chapter 3 — Approach Taken 23
(a) (b) (c)
(d) (e) (f)
Figure 3.1: Time series of a tortuos lightning channel with unknown spatial
distribution taken on 19 December 2010 at 02:52:42 − 0.930 s. (a) CC preceeding
ground flash (Reference time: +0 s) (b) CG discharge (+0.100 s) (c) +0.210 s
(d) +0.330 s (e) +0.660 s (f) +0.770 s.
a 3D model. Two investigations are conducted and compared in order to determine
the feasibility of reconstructing lightning discharge channel models using digital
images.
3.2 System and Evaluation
A system is designed and developed to accept digital images and associated camera
positions to render a 3D reconstructed lightning model. The scope of the study
includes testing the system against images obtained from laboratory-generated and
natural lightning discharge channels. The two investigations provide the test infor-
mation to determine the feasibility of the system for practical implementation on a
3D reconstruction of natural lightning attachment to tall structures. The study is
scoped to follow three distinct components.
1. System design (Chapter 4)
2. Testing: HV laboratory investigation (Chapter 5)
3. Testing: Physical lightning investigation (Chapter 6)
Chapter 3 — Approach Taken 24
The High Voltage (HV) laboratory investigation provides appropriate test data for
determining the validity of the system within a controlled environment and indicates
a preliminary small-scaled example of some difficulties in the setup of necessary
equipment. The nature of the controlled investigation provides the means of a
preliminary study to determine and correct for different camera positions. This
provides a small scale solution to the topic at hand.
The physical lightning investigation includes the reconstruction of two lightning
flashes to produce an accurate and usable reconstructed model. This investigation
includes more complication than the controlled laboratory environment in terms of
camera logistics, storage, and statistical predictability. This therefore limits the
number of discharges that can be reconstructed.
A feasibility study is developed from the individual investigations, for both single-
channelled and branched discharges. The success of the laboratory investigation
can potentially produce a 3D reconstructed discharge channel with acceptable error
margins from an image dataset obtained in a controlled environment. This acts as
a small-scale solution to the approach. The success of the physical investigation
produces a 3D reconstructed discharge channel from data captured from a naturally
occurring lightning strike. A comparison arising from the success criteria of the
two investigations allow for determining the feasibility of extending the system to a
real-world applications.
3.3 Contribution of this Dissertation
By obtaining a 3D representation of a discharge channel — either a HV discharge
or lightning, the channel can be properly analysed in 3D visualised space. The
motivation behind this research stems from the fact that lightning research has
previously been limited to 2D representations. Most 3D lightning models are based
from theoretical knowledge based on the work of Dellera and Garbagnati [26, 27] or
created for aesthetic purposes for digital media such as 3D games, movies and flight
simulators [29, 30, 33].
Chapter 3 — Approach Taken 25
3.3.1 Main Contribution
Due to the fast transient nature of the lightning event; a strike is difficult to fully
perceive with a naked eye; let alone in a 3D perception. Even with the photography
of certain strikes, the physical distribution and dimensions of the lightning channel
can only be assumed by channel or branch luminosity, which may differ depending
on the amount of charge associated with the branch in question.
A single photographed images only provides information in 2D, which limits eval-
uations of specific case studies, such as mentioned in Appendix B [22]. Current
research discussed in Section 2.2.2, consists of conventional 2D image capture of
lightning discharge channels for specified studies, which does not provide an accurate
spatial distribution of the channel. This generates a need to develop a system that
is capable of reconstructing a discharge channel within 3D space, providing a more
accurate spatial distribution of a channel, which is able to encompass its directional
data and split branches.
This research serves to be a stepping stone toward the reconstruction of 3D lightning
models. By constructing a 3D model of a discharge channel, a better understanding
of how the path of a large HV discharge channel or lightning flash develops its
pattern in a more comprehensive manner, which can provide more information to
better model the lightning channel.
In the case of lightning, a better understanding of the termination points, and the
(a) (b)
Figure 3.2: Demonstration of downward negative flashes that appear to be inter-
cepted by upward leaders from the ground. This is demonstrated by a sharp change
of direction in the channel path.
Chapter 3 — Approach Taken 26
striking distances can be evaluated. If a 3D model can be constructed of the lightning
flashes in Figure 3.2, the actual striking distance can be determined from the sharp
change in path direction, without inferring a distance based on its 2D representation.
3.3.2 Possible Extension to this Work
The use of 3D reconstructions of HV and lightning discharge channels provides
comprehensive details on the channel path over its duration. There are several
applications expected for reconstructed 3D discharge channels. This includes channel
tortuosities, as described in Gu et al’s application in which channel tortuosities are
calculated from a series of positive switching discharge channels [32]. Applications
also include the evaluation of striking distances of lightning flashes to tall structures
as discussed in Eriksson’s work [31]. This study can also be extended to electromag-
netic field simulations of a the propagation of the lightning path, given the known
3D co-ordinates of the lightning channel. Lastly, further extension can be applied
to time resolved lightning leader propagation provided several assumptions made
about the stepped leader lengths.
The following chapter defines the system designed for perform 3D reconstructions of
discharge channels. The photography of discharge channels and processing of images
is included as part of the system. The system also includes the reconstruction
algorithms used to produce models of a 3D nature from images and the relative
positions of cameras obtaining the images.
27
Chapter 4
System Design
A system is developed to capture images of High Voltage (HV) and light-
ning discharge channels at multiple perspectives and process the images
to render a reconstructed three-dimensional (3D) model of the discharge
channel. This chapter discusses the components of the system, including
the photography of the discharges, image processing to identify channel
information, extrapolation of 3D channel information, and testing and
evaluation methods.
4.1 System Overview
Figure 4.1: Block diagram demonstrating the three-dimensional reconstruction
system overview and flow.
An overview of the system and general flow diagram is presented in Figure 4.1. The
system includes the photography of discharges, image storage methods, synchroni-
sation issues, processing of images and relevant discharge information, and finally
rendering the data to a 3D model. The processing stages are presented, from image
insertion to producing a 3D model in an interactive user environment. For further
information on the ground-work for this system, refer to Appendix C [3]. The testing
of discharge channel image data used to validate the system capabilities is presented
in Chapters 5 and 6.
Chapter 4 — System Design 28
4.2 Photographic Equipment
The capture of image data takes into consideration the acquisition of image data
through a variety of cameras and optical filtering. This process includes the choice
of cameras used for discharge channel photography, management of the resulting
image data and optical filters that are required. Each subsection discussed in the
image capture component is described in Figure 4.2, which applies to all discharge
environments: HV or lightning discharges.
Figure 4.2: Discharge image acquisition using optical filters and cameras.
4.2.1 Data Filtering: Optical
Photographed images require only the intense light of the discharge channel in the
captured frame. For the purpose of this study, only wavelengths of the visible light
visible spectrum (380 to 750 nm) are required for modelling the discharge [34]. The
insignificant data needs to be filtered out; this includes the experimental environment
and additional glare occurring due to the discharge. Optical filters are used to obtain
usable data in the images. A combination of cross-polarised filters and camera
configurations provide images that can be used for the reconstruction. The use of
the filters is also widely dependent on the camera lens control capabilities.
The images in Figure 4.3 display the different captured image variation using differ-
ent layers of optical filters. It may be assumed that all images presented in this study
are filtered with any combination of these filters, unless otherwise stated. Figure 4.3a
shows the image captured of a lightning discharge channel without optical filters.
Chapter 4 — System Design 29
(a) (b)
Figure 4.3: Comparison of lightning images with different optical filter combinations.
These images are taken from separate lightning events with the same camera. (a) No
filters (b) Cross-polarised filters.
(a) (b) (c)
Figure 4.4: Comparison of high voltage discharge images with different optical filter
combinations. These images are taken from separate lightning events with the same
camera. (a) Cross-polarised filters (b) Cross-polarised and infrared filters (c) Cross-
polarised, infrared and violet filters.
It can be observed that the image is extremely overexposed. Two linearly polarised
lenses are placed perpendicularly to construct a cross-polarised filter, which reduces
the glare and intensity of light entering the lens. The image captured from this filter
is illustrated in Figure 4.3b.
In a HV laboratory environment, an additional combination of filters are used, due
to the close proximity of cameras to the discharge channel location. Figure 4.4a
demonstrates how cross-polarised filters do not sufficiently reduce the light entering
the lens. Additional infrared filters are used to reduce a portion of visible light
Chapter 4 — System Design 30
spectrum to the capture device. By using the infrared filter, the light in the
infrared spectrum is allowed through the filter. The image captured from this filter
is illustrated in Figure 4.4b. The violet filter is used to further reduce the light
wavelengths to the capture device. By using the violet filter, only the lower end
of the light spectrum is allowed to pass. The image captured from this filter is
illustrated in Figure 4.4c.
A disadvantage to using optical filters is the possible loss of image detail brought
about by damaged lenses but this is neglected for the purpose of this experiment.
The optical filters have also shown to produce reflections on some recorded images,
as shown in Figure 4.8.
4.2.2 Cameras
The traditional camera specifications are discussed in Section 4.2.3, in relation to
settings chosen for discharge channel photography. These cameras are disadvantaged
in the fact they they need to operate in unusual electromagnetic environments, and
these issues are discussed in Sections 4.2.4 and 4.2.5. Additional cameras features
are discussed in Sections 4.2.6 and 4.2.7. It should be noted that the camera settings
mentioned in this section are not all inclusive of the camera functionality, but merely
the configurations used for the purposes of this study.
A range of relatively low-cost Internet Protocol (IP) surveillance cameras from
Axis® Communications have been chosen [35]. The cameras have various advan-
tages regarding its configuration flexibility and additional features that standard
camera technology lack. Additional features include networking capabilities; remote
storage and triggering options, providing the capability to automate photography
of discharge channels [36, 37, 38]. A combination of four different Axis models (of
varying quantities) are used in a variety of applications. The four camera models
are listed below:
• Axis 207W
• Axis 207MW
• Axis M1011
• Axis P1344
Chapter 4 — System Design 31
This section discusses the cameras that have been used in this system, describing the
operation of each camera model and providing a summary of the camera usage and
status to date (refer to Table A.1 in Appendix A). It should be noted that the use of
different camera models may produce some differences in image quality and captured
information, therefore presenting mismatching information when comparing two or
three images of the same event. This may impact on the quality of reconstructed
models resulting from the system, but image processing steps are discussed in
Section 4.3 to minimise these image differences.
4.2.3 Camera Operation
All the camera models measure framerates in frames per second (fps), and have a
maximum framerate of 30 fps, although becomes limited with the use of an image
pre-buffer (described below). The 207W model has a maximum resolution of 640×
480, although the 207MW, M1011 and P1344 have options for higher resolutions in
the mega-pixel range. The cameras operate according to the settings as shown in
Table A.1 in Appendix A, but are described in further detail in this section.
An advantage to using a surveillance camera includes the ability to manage the cam-
era feeds from a single processing unit, specifically a laptop. The commununication
options are discussed further in Section 4.2.6. The cameras all have web interface
capability, which provides a live view of the camera feed and possibility of remote
triggering, assuming cameras are being monitored at the time. The camera settings
enable options for a timer pre-buffer and a post-buffer, which limits the amount of
data recorded. The pre-buffer function is essential for external triggering, as it is
only activated once the discharge has occurred.
Since the 207W model was the original camera model used, and the most limited in
functionality, many operational settings were callibrated according to this camera
model. The 207W Random Access Memory (RAM) limits the duration of the pre-
buffer to 2 s, which then operates at a framerate of 10 − 15 fps. The frame rate is
therefore used to optimise the buffer setting. For most discharges, it is expected
that only one image would capture the channel, but lightning discharges can have
durations lasting several microseconds, and therefore, being captured over several
frames.
To reduce the number of steps that need to be taken on image processing, the images
are set to record in greyscale, since only the intense white light from the discharge is
Chapter 4 — System Design 32
required. This option is readily available in all camera models except for the P1344
model.
4.2.4 Camera Safety in Laboratory Environment
The main concern with operating electronics in a high electromagnetic environment
(transients in particular), is shielding and electrical isolation of the circuits. This is
due to the transient behaviour of the discharge, which may introduce surges in the
circuit. With this in mind, fragile electronics, such as processing units need to be
protected from the surrounding area of the discharge. This is particularly important
to consider when operating a camera in the HV laboratory environment. Therefore,
this has an effect on the power options, data storage and general communications
to the camera.
The specific operations of camera safety is discussed in this section, and a summary
of the camera safety capabilities is provided in Table 4.1.
Table 4.1: Camera safety capabilities for operation in either the high voltage
laboratory or phyical lightning investigations.
Camera Communications Power Operation
Model Isolation Isolation Location
Axis 207W yes − lightning
Axis 207MW yes − lightning
Axis M1011 − − lightning
Axis P1344 yes yes HV/lightning
Electrical Isolation of Communications
The wireless option in the 207W and 207MW models provides an advantage in the
network connection through electrical isolation in the communications link. This
is important since the cameras do not have onboard memory, and need to store
recorded data to an external source. Therefore, by using the wireless option, these
cameras are unaffected by the transients through its communications link.
Chapter 4 — System Design 33
The M1011 operates much like the 207 range cameras, without wireless functionality.
The camera communicates only through an ethernet Local Area Network (LAN)
cable and stores to an external source, and therefore cannot be used within a
laboratory environment.
The P1344 cameras have on-board storage, through the use of a removable Secure
Disk (SD) card slot, and all components of the sensitive camera electronics are
enclosed in a metal casing.
Electrical Isolation of Power Supply
Using electrically isolated camera setups in the HV laboratory investigations are
necessary to adequately protect cameras from electromagnetic transients and stray
capacitances. All the camera models have an external input power option, with
additional ports for external triggering. Isolated power supplies have been used for
each of the camera models, depending on its model specifications, and limitations
and results are presented.
The 207 camera range and the M1011 camera have an input voltage with a small
range of variance of 5 ± 2% V [36]. Through an attempt to isolate the circuit with
a 5 V regulated power supply, it is found that the cameras require a high start up
current; which cannot be readily provided by a simple LM7805 regulator.
The M1344 cameras have variable input voltage range of 8 − 20 V. This allows the
usage of a common 12 V lead acid battery connected directly with the input terminals
to power an single camera in a HV laboratory. Small lead acid batteries are used
for portabilty of cameras to remote sites.
4.2.5 Camera Limitations in Functionality
It is important to note the limitations in the functionality of each camera model, in
relation to photographing discharge channels, as the images have a direct propor-
tionality to the quality of models that are produced. Common disadvantages of using
these cameras are that images get spliced and overexposure (or even underexposure)
of the lens with the use of an optical filter.
The 207 and M1011 camera ranges have additional limitations, in particular with
the photography of HV discharge channels in image quality, fixed iris and the
Chapter 4 — System Design 34
requirement for a network connection to record images. The use of the M1344
cameras reduce all the additional limitations.
Image Corruption
Due to the fast nature of a lightning flash, the shutter speed of the cameras become
significant. Although the cameras operate at 15 fps, which is considered a relatively
slow frame rate, the camera is often capable of capturing a full flash without
encountering an image splice produced by the shutter speed of the image refreshing
process. However, the shutter speed is shown to be finite with respect to the lightning
discharge event through the evidence of horizontal image splicing.
Figure 4.5: Image splicing for Axis 207W. Two subsequently occurring discharges
are captured between a frame change, Marker 1 indicates the bottom portion of the
first flash, and Marker 2 indicates the top portion of the second flash.
In Figure 4.5, two subsequently occurring downward negative discharges are pho-
tographed in one frame, indicated by Markers 1 and 2. Each discharge is missing
information due to the finite shutter speed with respect to the speed of this discharge
event. The offset of the shutter can be seen in the band between Markers 1 and 2.
In addition to the image splicing caused by the shutter speed, the P1344 model has
another process of corrupting the images as shown in Figure 4.6. From experimen-
tation, the cameras often record corrupted image data mostly in the pre-buffered
data. It is assumed that this has to do with file format encoding, and can only be
resolved through updating the camera firmware – at present this problem has not
been resolved in the firmware updates.
Chapter 4 — System Design 35
(a) (b)
Figure 4.6: Image splicing and pre-buffer induced corruption of information for Axis
M1344. Images are taken of the same discharge, 94◦ laterally separated. (a) Vertical
image splicing, (b) Vertical image splicing and pre-buffer corruption.
Overexposure
The cameras are intended for the purpose of capturing graphical discharge informa-
tion occurring at a set point, i.e. tower terminations. Discharges occurring in the
surrounding region of the termination point are often photographed by the cameras,
and can either be underexposed, or overexposed. The use of optical filters are used
to optimise the photography of discharges at the intended termination point.
(a) (b)
Figure 4.7: Overexposure for Axis 207W with the use of optical filters. (a) Overex-
posed frame (b) Normal frame of overexposed flash 20 ms after (a) is photographed.
Chapter 4 — System Design 36
However, the exposure of the lens during a lightning event will be discussed with re-
gards to surrounding flashes. The overexposed frame occurs occasionally, and whites
out the channel definition to unusable image information, as shown in Figure 4.7a.
A comparison of an overexposed frame with a normally exposed frame is shown in
Figure 4.7a and b. These images occur 20µs apart using the same camera.
Discharges that are underexposed may not provide enough of a change in pixels to
trigger the motion detection functionality in the cameras, and therefore not recorded.
These events may be assumed to be a little concern in this study.
Image Obstructions
The camera was situated indoors, behind a glass window, which would explain some
of the light distortions in some of the frames due to rain droplets. An example of
this can be observed in Figure 4.7b, indicated by the three rings of light close to the
position of the flash.
Additionally, the cameras are occasionally placed in positions where physical ob-
structions can be observed in the frame. It can be seen that in these cases, portions
of the lightning flash are obscured, and therefore limit the extent of the potential
models which can be reconstructed.
Surface Reflections
On some occasions, the images are corrupted by reflections of the channel. The re-
flections are either caused by windows (of indoor setups or outdoor camera housings)
or the optical filters place in front of the lens. Most images that obtain reflections
have a single ghosted reflection of the original channel. A double reflection is rarely
recorded on the image, as shown in Figure 4.8. In total, there are three resulting
reflections of the original channel, indicated by Markers 2, 3 and 4.
4.2.6 Network and Communication
Being IP cameras, the range of cameras all have an ethernet LAN connection for
communicating with the cameras from an external processing unit. This is the most
Chapter 4 — System Design 37
Figure 4.8: Channel reflections recorded on an image taken with the Axis 207W.
The number of the reflections depend on the intensity of the illuminosity, either
one or three reflections. Marker 1 indicates the original channel, Marker 2 indicates
the first reflection (more common), Markers 3 and 4 indicate reflections of 1 and 2,
respectively.
basic form of communication used with all the cameras for configuration, general
setup and maintenance.
External Storage
The 207 camera range, and M1011 require a connection to a network to operate as
required. In the HV laboratory, the 207 cameras are connected wirelessly to the
network. Cameras upload and store the recorded image feed through a File Transfer
Protocol (FTP) server to a specified directory on the network.
On-Board Storage
Cameras with on-board storage provide the opportunity for the camera to operate
without a network; i.e. server or dedicated processing unit. This means that cameras
can operate in remote areas, and only require a constant power supply.
The P1344 cameras have an option to use the on-board SD card slot. Maintenance
regarding the collection of data from SD cards is therefore dependant on the amount
of motion activity in the area and the size of the memory card.
Chapter 4 — System Design 38
4.2.7 Data Formats
The 207 range of cameras have an option to save its recorded feed to individual
Joint Photographic Experts Group - Image file format (JPEG) image files. Although
JPEG file formats tend to be more lossy than others, it serves the purpose that is
required of this study. This option allows for quicker file processing; as relevant
files can be readily identified and the modelling framework accepts JPEG formats
as inputs.
Although the M1344 cameras also have the same option to save individual JPEG
files, the usage of the on-board storage to SD card has limited the saved file formats
to a short video Matroska video (MKV) format. Therefore, all feeds from the M1344
require video-to-image conversions; and are converted to JPEG files for consistency.
4.3 Data Conditioning
The images needed be to filtered further so the channel information could be isolated.
Due to the greyscale ambiguities from the photographed images, digital filtering
was required. Once the images were filtered to explicit black and white images,
the relevant data was extrapolated from the images and conditioned to provide a
reconstructed model.
4.3.1 Pre-Processing of Discharge Channel Images
The application requires black and white images to extract the relevant pixels from
the image. By imitating a typical image of a discharge channel in its surrounding
environment, the lighter pixels represent the channel information, and the darker
pixels are regarded as redundant information. To ensure that the automated pro-
cesses involved with channel reconstruction do not encounter grey-pixel ambiguities,
the images are transformed into a Boolean image, where a white pixel (colour value:
255) represents a TRUE, and a black pixel (colour value: 0) represents a FALSE.
The image processing methods are programmed in Cplusplus (C++) for automata-
tion – with the use of Visualisation Tool-Kit (VTK) open-source libraries. The
documentation for VTK provides terminology that is used in this study [39]. The
term ‘filter’ is used to describe a process that accepts image inputs (single or multiple
Chapter 4 — System Design 39
images, depending on functionality), performs a task to change the input data, and
produces output images (single or multiple images) as a result. The image processing
filters are developed in an object oriented scheme. The digital filtering (or image
processing) provides a means to isolate the channel information. The images are
reduced in size for improving the processing efficiency of the rendering. Five filters
are used according to Table 4.2.
Table 4.2: Image processing filters using basic implementation of existing VTK
classes.
Filter Name VTK Class Implementation
Channel Identification vtkImageDifference
Black and White Boolean vtkImageThreshold
Smoothing vtkAnisotropicSmoothing2D
Merge -
Resize -
Tracking and Cropping vtkImageResize
Some images are manually processed, and then filtered again in the application.
Manual processing includes highlighting of certain qualities in images that may be
lost in the automated filtering processes. Digital filters are implemented before the
modelling stage to provide usable data for rendering a 3D model.
Channel Identification Filter
If a discharge channel is identified in a series of sequential images, shown in Fig-
ure 4.9, the series images is isolated and categorised by date and event number. Two
images before significant pixel change define the beginning of the series, and two
images after the pixel change defines the end. A sample of the resulting difference
image produced by the filter is shown in Figure 4.10.
The first image in the series, labelled by Marker 1 in Figure 4.9 is used to compare
iteratively with the rest of the series. This method of obtaining image comparisons
is due to the fact that thunderstorms can have durations of a few hours and ambient
environmental conditions may change significantly to cloud cover patterns or the
position of the sun. By implementing the comparison of images with an image
Chapter 4 — System Design 40
Figure 4.9: Channel isolation using image pixel difference comparisons with an image
occurring several frames before the channel is photographed. Marker 0 indicates the
fixed image, Markers 1−3 indicate images identified with significant pixel difference.
several frames before the occurrence of the lightning event, these environmental
changes can be ignored, and will not affect the identification of the lightning channel.
The difference filter produces a count of the number of pixels with a different colour
value. If a significant pixel difference is detected (as determined by the operator),
the resulting difference image is saved for further processing, as would be the case
for Markers 1− 3.
Black and White Boolean Filter
Once the difference image is produced, identifying the lightning channel still requires
some processing, since the channel is usually surrounded by a gray scatter. This filter
can also be known as the discharge channel isolation filter, as the purpose of this
filter is to provide the Boolean image as the input to reconstruction framework.
General images of discharge channels – in particular, lightning channels – range
from having very faint gray-scale channel definition to overexposure of the frame. A
pixel threshold level between 0 and 255 can be used to identify the lightning channel
information, where 0 represents black pixels and 255 represents white pixels. This
filter changes the image pixels to monochromatic shade, operating as a Boolean
filter, where any pixel above the selected threshold is changed to white pixel, and
below the threshold is changed to black.
Figure 4.11 demonstrates the use of the Black and White Boolean filter using
Figure 4.11a threshold value of 70 and Figure 4.11b threshold value of 100. It
can be seen that the lower the threshold values, the larger scatter noise that is
introduced into the image, as depicted in right channel of Figure 4.11a. Although
the higher threshold value, produces images with more limited channel information
Chapter 4 — System Design 41
(a)
(b)
Figure 4.10: Image difference of a lightning event occurring on 8 February 2011 at
18:13:47.900. (a) Original image (b) Difference image with a mismatch of 40, 063
pixels (of 600× 480 image resolution).
Chapter 4 — System Design 42
(a)
(b)
Figure 4.11: Black and White Boolean filter using threshold values between (0−255)
implemented for sample images used in Figure 4.10. (a) Threshold value of 70
(b) Threshold value of 100.
Chapter 4 — System Design 43
Figure 4.12: Smooth Bool process.
when the channel is thinner, as depicted in the right channel of Figure 4.11b.
Smoothing Filter
From Figure 4.11, it is seen that the hard threshold value produces an image with
specked channel definition for certain threshold values. This filter is designed to
smooth out the edges of the channel definition (according to an operator defined
scatter constant). In addition to smoothing out channel edges, this filter can diffuse
stray white pixels not connect to the channel. The use of this filter may require a
few iterations, depending of the quality of image that is photographed. The process
involved with using this filter is illustrated in Figure 4.12.
The drawback to using this filter includes the possible introduction of image errors
through the attempt to optimise the quality of image, such as introducing thicker
channel widths, or lost channel information. It is also a manually intensive process
that requires trial and error for optimising the channel quality. An example is shown
of the Smooth and Black and White Boolean filter combination used to optimise
channel definition in Figure 4.13. These images provide two iterations to illustrate
the purpose of the filter.
The alternative to using this filter is through manual processing of images, using
an image processing tool. This process is time-consuming and defining the channel
shape and definition is very subjective. However, manual image processing provides
a level of intelligence in determining channel shape, and can help to ensure that no
information is lost.
Chapter 4 — System Design 44
(a)
(b) (c)
(d) (e)
Figure 4.13: Smooth and Boolean filter iterations (a) Original image with focus area
labelled with Marker 1 (b) First iteration of Smooth filter with scatter constant set
to 5 (c) First iteration with Boolean filter with threshold at 90 (d) Second iteration
of Smooth filter with scatter constant set to 20 (e) Second iteration with Boolean
filter with threshold at 80.
Chapter 4 — System Design 45
Figure 4.14: Isolated images amalgamated in a single image to reduce timing issues.
Merge Filter
Some recorded events have limited time-resolved channels, which presents issues
with matching camera timing of different perspectives. To resolve this, all images
of the event are amalgamated into one single image. The resulting images would be
similar to an image captured if the camera exposure is kept open for the duration
of the event. The functionality of this filter is only used where necessary.
Once the series of images have been filtered to a Boolean image, the images are
loaded into a merge filter. Since input images are already in Boolean format, if a
pixel is represented by a value of 255 (white), it needs to be presented in the final
image. Each pixel is checked in each input image. If there is a white value in any one
of the pixels, the discrete output image map sets the corresponding pixel position
with a value of 255. The initial value for all each pixel in the output map is set to 0
(black). A simple demonstration of the function of this filter is shown in Figure 4.14.
Resize Filter
This filter is required to ensure that the channel information for each perspective
is sized correctly. The placement of cameras and the differing camera resolutions
result in images photographing discharge channels are different resolutions. This
resize functionality is performed manually in an image processing tool. This step is
important for the 3D reconstruction, as no intelligence is included in the algorithm
to account for mismatched channel sizes in different perspectives. The heights of the
white channel pixels are adjusted to the size of the image with the largest channel
resolution.
Chapter 4 — System Design 46
Tracking and Crop Filter
This is the last filter which is used as part of the data conditioning process and
requires all the input images for one channel reconstruction to perform its function.
This filter tracks the channel information from the images, and ensures that all
channel heights are the same. If they are not, the filter scales the images to fit the
largest channel height.
To reduce on computing memory and processing time, the set of images are sent
through the cropping filter. This is accomplished by reducing each image to an
identical size for the reconstruction process. This filter takes into consideration the
image orientation required of the individual image and rotates them individually,
according to user specified commands. This filter is constructed using four individual
developed classes.
4.4 Three-Dimensional Reconstruction Algorithm
The 3D algorithm is written in C++ programming language, with the use of VTK —
an open source, cross-platform visualisation toolkit. The application can reconstruct
a model with 3D definition using two or three images; each configuration may have
different options for reconstruction.
Using the VTK 3D environment demonstrated in Figure 4.15a, the filtered images are
arranged on a set of axes in 3D space, mapping the experimental setup. This is setup
through the reconstruction framework, which translates user defined commands to
necessary reconstruction environment preparation. The origin, (0, 0), of the setup
is representative of the centre of the setup. The images are placed in the relative
position as the original placement of cameras, facing the origin. The centre point of
the image is placed tangentially to the origin, offset by a user-defined radius.
The algorithm has been designed to process the setup in layers over the y-axis,
as shown in Figure 4.15b. This method eliminates the third dimension, reducing
the algorithm to a two-dimensional (2D) problem, as demonstrated in Figure 2.8b.
Normals of the white segments are projected to the centre of the setup, where they
are compared to the normals from other perspectives. Each layer of the discharge is
assumed to have a cylindrical body. The centres of two images determine the centre
point of the cylinder, where the average thickness of the images determine the radius
Chapter 4 — System Design 47
(a) (b)
Figure 4.15: A simple branched channel generated as an example to illustrate
the image placement in the reconstruction environment. (a) Reconstructed model
about environment origin surrounded by images contributing to its reconstruction
(b) Zoomed view illustrating the stacked nature of the model design.
of the cylinder. The third image is used to verify the existence of the cylinder for
branched channels. In the example provided in Figure 4.15, the mirrored image of
the channel definition placed 180◦ provides the verification required for branched
channels.
4.4.1 Limitations of Model Reconstruction
There are several factors that limit the accuracy and the resulting detail of the
reconstructed models. Since the accuracy cannot be easily determined, due to the
fact that direct comparison cannot be made with the original discharge channel,
this level of accuracy cannot be quantified. Therefore, the accuracy can only be
determined with reference to the photographed images.
The limitations dictating the accuracy of the reconstructed model are identified and
noted using an example of two perspectives of a captured lightning flash, Figure 4.16
and Figure 4.17. The first perspective is labeled with reference to Camera 1 as shown
in Figure 4.16 taken at 0◦ and the second perspective is referred to as Camera 2 as
shown in Figure 4.17 taken at a lateral separation of 34◦.
Chapter 4 — System Design 48
Model Resolution
The accuracy of the reconstructed lightning model is soley dependent on the quality
of image input into the system. For images with low resolution, limited lightning
information can be obtained from the image, and slight variations in the channel
shape can be missed in the reconstructed model.
(a) (b) (c)
(d) (e) (f)
Figure 4.16: Camera 1 — Timing inconsistencies capturing different levels of
information, in particular, Frame 2 producing branching information not evident
in any other frame of the event. (a) Frame 1, (b) Frame 2, (c) Frame 3, (d) Frame 4,
(e) Frame 5, (f) Frame 6.
(a) (b) (c)
Figure 4.17: Camera 2 — Matching lightning event captured 34◦ from Figure 4.16
at a lower image resolution. (a) Frame 1, (b) Frame 2, (c) Frame 3.
Chapter 4 — System Design 49
The image resolution is based on the camera resolution and the distance away from
the discharge location. In the laboratory investigation and the physical investigation,
a combination of different cameras and different distances from the discharge are
utilised. The difference in photographed channel resolution requires scaling of
images. In most cases, images with lower resolution are enlarged to match the
size of the high resolution images. This results in crude channel definition on the
lower resolution image, and likely introduces a loss of channel definition and thicker
reconstructed channels.
With reference to the set of images taken from a single CG lightning event, Camera 1
resolution produces a channel height (from cloud to ground) of 155 pixels, whereas
Camera 2 resolution produces the same channel in 54 pixels. This results in a scaling
ratio of almost 1 : 3.
To demonstrate this point, a comparison of Camera 1, Frame 2 in Figure 4.16b and
Camera 2, Frame 1 in Figure 4.17a. In the perspective of Camera 1, it can be seen
the branching information has been captured, but in the perspective of Camera 2,
a hint of branching can be seen, but cannot be properly defined. This therefore
limits the model to only reconstructing the return stroke of the channel due to the
limitation of image comparison.
Quality of Input Boolean Images
The automation of image conditioning may result is the loss of significant lightning
information. It may also result in the introduction of greyscale noise, depending on
the chosen image threshold. In addition, the thickness of the channel in the Boolean
image is partially determined by the threshold limit, and has a direct effect on the
reconstructed model.
Synchronisation of Camera Information
Using multiple cameras, the information photographed may not capture the same
level of channel detail due to unsynchronised devices. In the reconstruction of
discharge channels, matching of camera images from different perspectives usually
results in the loss of some channel detail. This drawback is partially resolved through
merging the time-series images into one single frame, as described in Section 4.3.1.
Chapter 4 — System Design 50
The problem with this method appears if one camera does not capture any signficant
information in certain branches.
4.4.2 Two-Image Reconstruction
The basic reconstruction algorithm implementation is shown in Figure 4.18, for
an example of two images placed at 90◦ separation. The center of the channel
segment is determined by the intersection of the center normals and the radius of
the channel segment is determined by averaging each center intersection with the
outer image segment borders. Labels are annotated on the figure for reference to
variables discussed in Equation 4.1.
Rcs = r1 + r2 + r3 + r44 (4.1)
where
Rcs = Radius of channel segment, pixels
rn = Radial distance from segment center normal intersection point,
where n = {1, 2, 3, 4}, pixels
Figure 4.18: Basic channel reconstruction algorithm for single-channelled discharges,
resolving channel segments by a series of two-dimensional geometric problems.
Chapter 4 — System Design 51
The use of two images for reconstruction limits the model to a single channelled
discharge. This is due to certain redundancies that occur when branches are
introduced, which is described in more detail in Figure 4.19.
4.4.3 Three-Image Reconstruction
For three images, the algorithm used to reconstruct the models is altered to suit an
additional image. The main use for three-image reconstruction is the resolution of
channel branches. In Figure 4.19a, if there are branched structures in the images,
there are four intersections of the normals, defining four channel centers in the
model. This redundancy is resolved with the use of the third image, as shown in
Figure 4.19b.
In addition, Figure 4.19b demonstrates the ideal case for images that are placed
in the perfect eye-level position in relation to the channel model. This algorithm
represents the case that all normals intersect in one co-ordinate. Since center normals
are defined by the channel width and position in the image, this coordinate is often
variable depending several factors, including the camera exposure and the level of
filtering, and the image quality.
The real case for reconstructing channels using three input images in this framework
cannot use this algorithm as it stands, since placement of input images cannot be
exactly matched from the original camera perspectives. Therefore, a compromise
is made, by using the third image to resolve redundant channels in the setup.
The problem with using this technique is the decision on which images get used
for the channel reconstruction, and which one image is used to resolve redundant
channels. Therefore, the algorithm currently stands at using all the information,
each image taking a turn at resolving redundant channels, and merging the resolved
channels together, as shown in the process presented by Figure 4.20a-c). Table 4.3
summarises steps shown in resolving each channel segment with reference to the
figure illustrations. Each resolved channel is labeled by the resolving image, for
consistency. For example, resolved channel C1 is resolved by intersection of I1 and
constructed using information from I2 and I3.
The constructed channel segments have two options for reconstruction: first detect
and segment averaging. First detect option constructs all three resolved channel
segments, C1, C2 and C3. This is demonstrated in Figure 4.21, using resolved channel
segments in Figure 4.20. If the first detect option is not used, then assuming that
Chapter 4 — System Design 52
(a)
(b)
Figure 4.19: Redundancies for branched channels from images. (a) Two branches are
assumed as part of the channel, and two are assumed by be redundant (b) Resolving
channel branch redundancies using a third image.
Chapter 4 — System Design 53
(a) (b)
(c)
Figure 4.20: Algorithm for constructing channel segments from three images to
resolve channel redundancies, using the third image as verification (a) Construction
of C1 using I1 for verification (b) Construction of C2 using I2 for verification
(c) Construction of C3 using I3 for verification.
Table 4.3: Three-image reconstruction algorithm steps to reconstructing channel
segments for first detect option.
Cylinder Resolving Reconstruction Figure
Number Image Images Reference
C1 I1 I2 & I3 Figure 4.20a
C2 I2 I1 & I3 Figure 4.20b
C3 I3 I1 & I2 Figure 4.20c
Ctotal all all Figure 4.21
Chapter 4 — System Design 54
Figure 4.21: Channel segment constructed from resolved channel segments C1, C2
and C3 from Figure 4.20 if first detect option is true.
the reconstruction algorithm processes images in the order of I1, I2 and then I3,
image information from I3 is only used to verify the existance of a channel segment,
and therefore C3 is constructed as part of the model, as shown in Figure 4.20c.
The use of this option in the algorithm presents inconsistencies in the reconstructed
discharge channel, whichever option is chosen.
The segment averaging option averages the locations and radii of resolved channel
segments per y-axis iteration of the reconstruction and constructs only one channel
segment in each iteration. The use of this option is best for the reconstruction of
single channelled discharges. This option can either be set to TRUE or FALSE, in
conjunction with the first detect option. In total, there are four different options
configurations that can be used in the reconstruction of models using three-image
inputs.
Chapter 4 — System Design 55
4.5 Testing Framework
There are seven reconstruction algorithm options, which are listed in Table 4.4
(adapted from [3]). Branching definition can only be reconstructed with the avail-
ability of three images, and the average option may not be used for any branched
image information. The first detect option can be used to reconstruct for all cases.
Table 4.4: All seven algorithm options available for individual reconstruction cases
for two or three image reconstructions.
Case Images Branching Average First Detect
001 I1, I2, I3 False True True
002 I1, I2, I3 False True False
003 I1, I2, I3 True/False False True
004 I1, I2, I3 True/False False False
005 I1, I2 False – True
006 I2, I3 False – True
007 I1, I3 False – True
In order to quantify the accuracy of resulting models, the corresponding images of the
model are used for pixel matching of channel information with the original Boolean
image. This comparison is achieved using a tester application. This comparison is
shown with two arbitrary shapes in Figure 4.22. An image difference is produced
from the tester application, which identifies the pixel mismatch between the two
images. The number of mismatched pixels is also provided as pm. Equation 4.2
provides the error calculation for the model verification.
Epm = εpmIh × Iw × 100 (4.2)
where
Epm = The percentage error of mismatched pixels, %
pm = The number of mismatched pixels, pixels
Ih = Height of the tested images, pixels
Iw = Width of the tested images, pixels
Chapter 4 — System Design 56
(a) (b) (c)
Figure 4.22: Testing procedure comparing pixel mismatching of two images (a) Circle
(represents original Boolean image) (b) Square (represents image of model at same
perspective) (c) Difference between the two images indicated by white pixels.
The height and width of the compared images must be identical in order for this
comparison to obtain successful results. It should be noted that the error calculation
takes into account the total error of the entire image, and not only of the significant
channel information. This may provide a misleading result, since the calculation is
a function of the image size (which includes the majority black pixels).
The arithmetic testing method does not provide a pixel-by-pixel matching accuracy,
and comparison of reconstructed channel paths. Additionally, model accuracies are
determined visually by a manual case-by-case analysis. The accuracy of recon-
structed models will examine three properties: channel shape, continuity and the
presence of significant channel duplication.
4.6 Conclusion
The system designed to reconstruct discharge channels in 3D is completely modular.
A simple summary of the stages required for the system to operate includes the
photography of discharges from several perspectives; image processing to isolate
the channel information; inferring the information to 3D cartisian co-ordinates; and
testing the accuracy of the resulting models.
The photographic equipment describes the use of Axis cameras and a combination of
cross-polarised, infrared and violet optical filters. The cameras provide an automatic
triggering functionality and the optical filters reduce the glare of the fast transients
preventing overexposure of the image.
Chapter 4 — System Design 57
Once images of the discharges are acquired, data conditioning needs to be performed
to produce Boolean images. The Boolean images required represent white pixels as
channel information, and black pixels as redundant information. This is obtained
through a combination of digital filters developed in C++ and VTK: channel iden-
tification; black and white Boolean; smoothing; merge; tracking and cropping; and
resize filters.
The 3D reconstruction of the discharge channels requires the inputs of Boolean
images and the respective angular separation of the camera perspectives about the
channel location. The algorithm used to extrapolate the 3D information simplifies
the problem to a series of 2D geometric calculations. One-pixel high channel
segments resulting from the 2D geometric calculations are stacked to produce the
discharge channel shape and structure.
Two main algorithms are implemented; two-image and three-image reconstructions.
The two-image reconstruction algorithm is designed as the simplest form of the
algorithm intended for single-channeled discharges. The three-image reconstruction
algorithm is designed to reduce redundancy on branched discharge channels. Each
algorithm has a set of configurations defining options first detect and average to
either TRUE or FALSE.
The testing framework defines a comparison between the Boolean input image, and
the matching image perspective of the reconstructed model. Two methods of testing
are defined, an arithmetic method in comparing the level of mismatch between
images and visual testing.
The following chapter describes the first step in the evaluation of the system perfor-
mance under laboratory conditions. This is the first set of evaluations made on the
system capabilities in reconstructing HV discharge channels, providing insight into
the performance of the system and its reconstruction algorithm configurations.
58
Chapter 5
HV Laboratory Investigation
A series of small scale tests are performed in the HV laboratory, as
a proof-of-concept to reconstructing discharge channels for lightning.
The small scale tests help to identify and replicate some challenges
expected in the large scale lightning investigation. With the successful
reconstruction of laboratory discharge channels, confidence can be gained
in reconstructing large scale lightning discharge channels.
5.1 Overview
This chapter describes small scale testing on the reconstruction of discharge channels
in a controlled laboratory environment. Although the purpose of this investigation
extends to the reconstruction of lightning discharges, it has been found that monitor-
ing high voltage testing procedure using video recordings is a useful tool for gathering
information on unexpected failure, since burn marks, damaged insulation and carbon
by-products are usually the only visual indication of failure due to flashover. Even
in the presence of a human operator, the failure can escape the the naked eye and
the full extent of the damage may not be perceived. Therefore showing that the
reconstruction of high voltage laboratory discharge channels has its own merits.
Several gap configurations are investigated, with different combinations of camera
positions. The system is also tested with the photographed information under all its
different configurations. Each experiment is briefly discussed, including the gap con-
figuration setup, camera combinations and positions, resulting reconstructed models
and the contributing factors from each experiment. Each individual experimental
Chapter 5 — HV Laboratory Investigation 59
setup modularly investigates different aspects of the reconstruction problem and
provides insight and confidence into the system capabilities:
1. Experiment A-1: General investigation
2. Experiment A-2: Single-channel verification
3. Experiment A-3: Branched-channel evaluation
For additional information on work performed regarding laboratory discharge chan-
nels, refer to Appendices. The work discussed in Appendix C introduces the
preliminary testing performed using HV discharge channels discussed further in
Experiment A-1 [3]. The work discussed in Appendix D provides an investigation
into large discontinuous laboratory gaps using two higher resolution cameras [40].
Lastly, the work discussed in Appendix E provides an overview to preliminary
investigations into reconstructing channels from different camera heights [41]. From
the investigation, it is concluded that camera angles below eye-level in the range of
0−18◦ provide inconclusive results, due to the absence of a third camera perspective
to provide validation of channels.
The advantage to testing small scale experiments in a high voltage laboratory is the
fact that testing is done in a controlled environment. Although this may seem trivial,
it is important to iteratively test the capabilities of the cameras in the presence of
high transient electromagnetic fields. As identified in Section 2.2, lightning has
multiple unknown variables associated with its formation and appearance. The
controlled environment allows for the prediction of several unknown characteristics
such as providing:
• a predetermined position of a discharge (governed by the gap geometry);
• an approximated length of the discharge channel (determined by the gap size);
• a predictable time to flashover (given by the voltage level and gap geometry);
and
• flexible camera positions relative to the discharge channel (due to the scale of
the laboratory environment with relation to a large scale lightning investiga-
tion).
Although the propagation of lightning is governed by the leader mechanism, which is
more closely replicated by a switching impulse over a gap of more than 10−30 meters,
Chapter 5 — HV Laboratory Investigation 60
with long front times (in the order of hundreds of microseconds) [26], the small scale
testing of discharge channel photography is achieved by flashing over a large air
gap with the use of voltage impulses. These voltage impulses are produced by a
multi-stage impulse generator (or Marx Generator) and are typically used to test
the induced effects of lightning or operational surges of protection equipment. As
a proof of concept, a voltage impulse over a large air gap can produce a highly
illuminated discharge channel, which sufficiently replicates the visual effects that
are required for this investigation.
5.2 Experiment A-1: General Investigation
The focus of this experiment is to determine how many cameras, and which camera
positions would produce the best 3D reconstructed models. A direct comparison of
the two-image and three-image reconstruction algorithm is also obtained across the
board of all photographed datasets. This is discussed in more detail in Section 5 of
Appendix C [3].
5.2.1 Experimental Setup
A rod-to-rod gap configuration with a gap length of 0.83 m was used, which de-
termines the height of the discharge channel. The rod-to-rod configuration usually
gives rise to single-channelled discharges, although occasionally branched channel
are observed. The breakdown voltage in air was obtained at approximately 550 kV
with the given gap configuration. The general setup in the high voltage laboratory
is provided in Figure 5.1. Three wireless cameras from the Axis 207 range are used
at equal distances from the gap configuration. The wireless cameras communicate
with a local laptop via an ad-hoc network; and all triggered information is saved
directly to the laptop.
The cameras were placed in several angular formations to determine the ideal camera
angles for three-dimensional reconstruction of the system. There are five angles that
were tested: 30◦, 45◦, 60◦, 90◦, and 120◦ as shown in Figure 5.2, which provided a
wide range of angles to evaluate.
Several additional factors needed to be taken into consideration: location, height,
distance, and angles. The location of each camera was important to consider for
Chapter 5 — HV Laboratory Investigation 61
Figure 5.1: Experimental setup for laboratory Experiment A-1 to determine the
optimal camera positions for reconstruction — Current camera configuration at 45◦.
protection purposes. The cameras were therefore place at a radius of 1.7 m away
from the gap setup, or Device Under Test (DUT). Each of the cameras were placed
at the same height above the ground of 1.035 m, which is also the same height as
the grounded rod electrode at the base of the DUT setup.
5.2.2 Reconstruction Results
Two sets of images were photographed from each camera angle configuration, result-
ing in a total of ten image datasets. Using Equation 4.2, the pixel mismatch error
(Epm) calculated from this dataset was determined at 11%, and the optimal angular
separation for camera positions was 45◦. This information was taken from a small
dataset, and an error calculation that includes a large redundancy. Additionally,
many modelled reconstructions produced mismatched channel paths, mostly due
to input images having mismatched channel sizes. Despite the measured camera
positions from the DUT providing similar gap lengths in the camera frames, this
size mismatch still played a large factor.
Chapter 5 — HV Laboratory Investigation 62
(a) (b)
(c) (d)
(e)
Figure 5.2: Three-camera angular separations for Experiment A-1 (a) Camera
separation of 30◦ (b) Camera separation of 45◦ (c) Camera separation of 60◦
(d) Camera separation of 120◦, and (e) Camera separation of 90◦.
Chapter 5 — HV Laboratory Investigation 63
5.2.3 Discussion
The testing procedures used to analyse these image sets does not provide a com-
prehensive measure of the reconstructed model accuracy. Visual analysis still needs
to be performed in each case, as provided in Table 5.1. Each reconstruction case
(as specified in Table 4.4) is examined for all ten image datasets. The correct
channel path is determined through visual comparison, and direct pixel matching
has not been implemented for this observation. The presence of missing channel
segments and significant channel duplication may mean that the images are mis-
aligned. Cases 001 − 004 provide three images per dataset, since all three images
are involved in the reconstruction. Cases 005− 007 include two images per dataset,
although Case 007 lacks two sets of data for 90◦ camera separation, as using images
at 0◦ and 180◦ would not provide a relevant model.
Table 5.1: Visual evaluation of all laboratory datasets providing number of
reconstructed images containing the listed characteristics.
Case True or Correct Missing Significant
No. False Path? Segments? Duplication?
001 True 23 3 0
False 7 27 30
002 True 21 21 0
False 9 9 30
003 True 15 0 21
False 15 30 9
004 True 15 18 12
False 15 12 18
005 True 20 2 –
False 0 18 –
006 True 14 0 –
False 6 20 –
007 True 16 2 –
False 0 14 –
Chapter 5 — HV Laboratory Investigation 64
The information presented in Table 5.1 can to identify some specifics about how
the algorithm configurations perform on a specified dataset. It can be seen that for
visually matched channel shapes, the averaging option provided by Cases 001 and
002 reconstructs models that give the approximate shape of the channel expected
to be reconstructed. However, this is only visually matched, and any further
investigation into the precision of the channel segment locations could result in
a considerate deviation in position. If the averaging option is not used, there is a
50% chance of achieving the correct channel path, which is offset by an observation
of significant duplication of the channel branches, where only a single (or one split)
should exist. Although it can be seen that for best reconstructions, only two images
should be used, as observed in Cases 005− 007.
For best continuation of the reconstructed channel path, the first detect option
provides the best results, as shown in Cases 001 and 003. This option ensures
that any channel segment that is verified gets reconstructed as part of the channel
and provides minimal missing segments, as shown in Figure 4.20. Additionally, the
first detect option is seen to provide good channel continuation in the two-image
reconstructions in Cases 005− 007. This option can produce branching information
from two image reconstructions, although it has a 25% chance of being the correct
branch combination for a single split branch.
5.3 Experiment A-2: Single-Channelled Verification
With the use of three cameras in single channelled discharge testing, it is possible
to perform model verification tests to determine the accuracy of the reconstructed
model. This is accomplished by reconstructing the channel with two perspectives,
and using the third image for comparison at the respective perspective.
5.3.1 Experimental Setup
This evaluation uses images taken from the setup discussed in Section 5.2. A sample
of three original image perspectives photographed from 120◦ camera separation is
used to demonstrate the method of analysis and is provided in Figure 5.3.
Chapter 5 — HV Laboratory Investigation 65
(a) (b) (c)
Figure 5.3: A set of images samples taken in the high voltage laboratory investigation
with three camera perspectives at eye level (a) Camera 1 at 0◦ (b) Camera 2 at 120◦
(c) Camera 3 at 240◦.
5.3.2 Reconstruction Results
The model is reconstructed for image perspectives of 120◦ apart, as shown in
Figure 5.4. Verification is performed from the image taken at 240◦ demonstrated in
Figure 5.4c. This perspective is chosen as the verification image due to the curved
channel shape seen at this perspective, and not represented directly in the other two
images. If the reconstructed model can replicate the curved channel shape as seen
in the image from this perspective, it can be assumed that single-channel recon-
struction only requires the use of two images. This would also provide verification
that reconstructed discharge channels using the single-channel algorithm correctly
reconstructs models given the images and corresponding angular separations.
5.3.3 Discussion
A direct comparison is made at the 240◦ perspective between the channel information
taken from the original image, the filtered image and the reconstructed image
of the model without direct input from the original perspective. The original
image is presented in a cropped form in Figure 5.5a, the filtered image of the
third perspective is shown in Figure 5.5b, and the reconstructed model at the
corresponding perspective is produced in Figure 5.5c. The reconstructed model
has an underlying image (in the background of the model) of the original channel
shape (thinned version of Figure 5.5b).
Chapter 5 — HV Laboratory Investigation 66
(a) (b) (c)
Figure 5.4: Reconstructed model from Figure 5.3. Input data can be seen behind
the model channel, to match the accuracy of reconstructed channel path and shape
for Cameras 1 and 2. (a) Camera 1 at 0◦ (b) Camera 2 at 120◦ (c) Perspective of
reconstructed model at 240◦.
(a) (b) (c)
Figure 5.5: Verification through comparing third photographed image from Cam-
era 3 at 240◦, not used as an input for the model reconstruction. (a) Original image
(b) Boolean image (c) Reconstructed model at corresponding angle (background
underlay of channel shape of original channel, for direct comparison).
Chapter 5 — HV Laboratory Investigation 67
It can be seen that the reconstructed model follows the shape of the third verification
image, without the use of the original image as input data. The top portion of the
channel follows the correct shape, which includes the stepped bevelling along the
channel above the curve. Although at the top of the channel, the direction is tilted
towards the right with respective to the observed perspective. This implies that there
may be camera lens curvature that would need correction, or one of the cameras may
be placed at a slight tilt. This may be explained by the fact that cameras are placed
at the same level as the ground electrode, and the focal points of the cameras are
tilted slightly upwards. This should be corrected with subtle image normalisation.
Nonetheless, the bottom down appears to correctly follow the original shape without
any significant offset. Therefore, this evaluation has provided some confidence in the
two-image reconstruction algorithm.
5.4 Experiment A-3: Branched-Channel Evaluation
Most discharge channels have branched characteristics, and lightning discharge
channels no exception. It should be noted that branched channels can only be recon-
structed using the three-image reconstruction algorithm described in Section 4.4.3.
If only the two-image reconstruction algorithm is used with the first detect option,
branched definition could be reconstructed, but the resolved paths have a one in
four chance of being correct. This investigation focuses on laboratory discharge
channels with 3D spatial definition, and the use of two and three perspectives to
reconstruct the model. Furthermore, this investigation evaluates the capabilities of
the three-image reconstruction algorithm.
5.4.1 Experimental Setup
This evaluation uses images taken from the setup discussed in Section 5.2. Since
branched channels occur rarely in a rod-to-rod gap setup, only one discharge is
discussed. The three Boolean images photographed for this discharge were taken
at a 45◦ camera separation. Two models are reconstructed: a two-image model
(Part 1) and a three-image model (Part 2). Table 5.2 provides a summary of the
model configurations in each part.
Chapter 5 — HV Laboratory Investigation 68
Table 5.2: Reconstruction configurations for branched HV discharge channel
evaluation using two- and three-image algorithms.
Property Part 1 Part 2
Images Used I2, I3 I1, I2, I3
Angular Separation 45◦ 45◦
Model Configuration Case 006 Case 004
First detection setting true false
Average setting false false
5.4.2 Reconstruction: Part 1
Two of the three images are used for this investigation, I2 and I3 (or Case 006). The
Boolean images are provided in Figure 5.6a and c. These two images were chosen for
the significant branching detail that is required to resolve branched channels using
the first detect option.
(a) (b) (c) (d)
Figure 5.6: Reconstructed model of branched HV discharge channel using two input
images. In each pair, shows the resulting Boolean image (left), and corresponding
perspective of the reconstructed model (right) (a-b) Perspective 2 at 45◦ (c-
d) Perspective 3 at 90◦.
From the reconstructed images in Figure 5.6b and d, it can be seen that reconstructed
model paths match the original images. But despite the fact that two-image recon-
structions for branched images can produce visually accurate models these models
Chapter 5 — HV Laboratory Investigation 69
reconstruct an ambiguity and may not yield accurate branched paths. Therefore,
the presence of this ambiguity means that models from this type of reconstruction
cannot be used for accurate analyses.
5.4.3 Reconstruction: Part 2
This example presents Case 004 for the model reconstruction and is shown in
Figure 5.7. The images show the Boolean image placed on the left of each pair
and the corresponding perspective of the reconstructed model is on the right. The
reconstruction modelling parameters are indicated in Table 5.2.
(a) (b) (c) (d) (e) (f)
Figure 5.7: Reconstructed model of branched HV discharge channel. In each pair,
shows the resulting Boolean image (left), and corresponding perspective of the
reconstructed model (right) (a-b) Perspective 1 at 0◦ (c-d) Perspective 2 at 45◦
(e-f) Perspective 3 at 90◦.
The model presented in Figure 5.7 appears to generally follow the channel path
given the specific perspective matching.
5.4.4 Discussion
If a direct comparison is made on the channel paths reconstructed from the investi-
gations in Part 1 and Part 2, as shown from a similar arbitrary perspective of both
reconstructed models in Figures 5.8 and 5.9, it can be seen that there is a significant
difference in the branched paths the model reconstructed. This is explained by
Chapter 5 — HV Laboratory Investigation 70
(a) (b)
Figure 5.8: Image of the two-image reconstructed model at an arbitrary perspective
indicating inaccurage branching definition. (a) Full length with marked focus
(b) Zoomed image of marked focus.
the fact that two-image reconstructions using the first detect option resolves the
first channel segment per center normal, and therefore reduces the reconstructed
ambiguity. However, this is does not yield accurate models.
Therefore, branched definition can only be accurately defined by a third image
perspective. Despite the fact that reconstructed models using three-images, the
models are not perfect. Upon closer inspection as indicated by Figure 5.9, it
is seen that the reconstructed model has two major flaws: reconstructed channel
discontinuity and duplicated branches in the branch split.
It is difficult to produce perfect camera positions in the laboratory without spe-
cialised equipment, and slight tilts and inaccuracies can reflect in the reconstructed
models through meshed duplication of branches or missing segments. In addition,
limitations in the reconstruction algorithm and current framework can also be a
contributing factor. For the branched channels to be accurately modelled using
this algorithm, the framework could include some intelligence to properly align the
images, such that corresponding channel information can be matched properly to
avoid discontinuities and duplicated branches. It is noted that input images of two
pixels or less would result in discontinuities, due to the lack of valid normals being
extended from the image data. This means that refinement on the current modelling
algorithm may be required in future.
Chapter 5 — HV Laboratory Investigation 71
(a) (b)
Figure 5.9: Image of the three-image reconstructed model at an arbitrary perspective
indicating duplicated channels per branch and missing segments. (a) Full length with
marked focus (b) Zoomed image of marked focus.
5.5 Conclusion
This investigation has provided some confidence in the system capabilies in pro-
ducing 3D reconstruction of HV laboratory discharge channels. Each successful
reconstructed model has provided a small-scale proof-of-concept to reconstructing
discharge channels in a controlled environment. Although model accuracies cannot
be fully determined through a comparison with input images, confidence is gained
through a direct comparison between image perspectives of reconstructed models
and the original Boolean images. This comparison provides a good indication to
determine the accuracy of the model from each known perspective.
The difference in algorithm configurations have been tested against a set number
of images taken at different angular separations. All datasets obtained contain
three image perspectives at a set angular displacement. It has been shown that
by averaging the channel segments per y-axis iteration, generally correct channel
paths can be obtained. This is determined by visual comparison and the resulting
models may not necessarily be used for a detailed analysis. It is noted that this
may not be accurate enough for research purposes. The first detect option for three-
image reconstructions provides better channel continuation, but also increases the
Chapter 5 — HV Laboratory Investigation 72
channel duplication of the model. These errors may be indicative of slight image
mis-alignment.
The two-image reconstructions of single-channelled discharges provide accurate chan-
nel paths, good channel continuation, and no channel duplication. Additionally, the
models have been verified using a third perspective matching. It has been seen that
complicated channel paths have been duplicated in the third perspective comparison,
although it is evident that there is an offset on the channel tilt. Cameras are placed
at the same level as the ground electrode, and the focal points of the cameras are
tilted upwards.
The best branched definition is reconstructed using Case 004 (no first detect and no
averaging), which minimalises the redundant duplication of branches. Nevertheless,
duplication of channel branches cannot be completely eliminated, given that camera
perspectives cannot be perfectly matched according to required spatial specifications.
Additional intelligence to the framework functionalities can be incorporated to
ensure that reconstructed models are optimised. The averaging option may not be
used to reconstruct branched definition. Additionally, using the first detect option
for two-image reconstructions can provide some branching definition, but has a 25%
chance of providing accurate branching locations.
Now that the system has successfully reconstructed small-scale laboratory discharges,
the following chapter describes a preliminary investigation into the reconstruction
of single-channelled and branched lightning discharges.
73
Chapter 6
Physical Lightning Investigation
A series of tests are performed to reconstruct lightning image data
to 3D models of the photographed discharge channels. An evaluation
is performed on preliminary tests of single-channelled and multiple-
channelled (or branched) lightning discharges.
6.1 Overview
This chapter describes a preliminary investigation into reproducing the 3D details
of full-scaled lightning discharges, taking into account the simple single-channlled
discharge, and the more complex branched case. Image data is obtained from other
researchers (with their permission). The following investigations are discussed in
this section:
1. Investigation B-1: Single channel (Tuscon)
2. Investigation B-2: Multiple channels (South Dakota)
A preliminary investigation was performed on one branched Cloud-to-Cloud (CC)
lightning channel in Appendix F [42]. Since only one perspective was obtained, no
3D definition could be reconstructed. The model reconstructed was a flat channel
that was reconstructed in 3D space, and correctly constructed the branched channel
definition. This preliminary study provides some confidence in the reconstruction
algorithm and its ability to reconstruct multiple branches in a channel.
Chapter 6 — Physical Lightning Investigation 74
It should be noted that the camera elevations have not been taken into account
in the reconstructions of these lightning channels, as proper analysis has not been
performed in the laboratory investigation. The evaluations of the reconstructed
lightning models should all be noted with a possible error due to omission. Future
evaluations can be performed with elevation correction and used to compare with
the results found in this section.
6.2 Experiment B-1: Single Channel (Tuscon)
In this investigation, a single-channelled lightning discharge channel is reconstructed
using images taken from Dr. Saba in 2007 [43]. Two successive flashes, with different
channel shapes, were photographed with this setup. An example of one of the
recorded lightning flashes is discussed in Appendix G. This section discusses the
second photographed flash.
6.2.1 Experimental and Setup
(a) (b)
Figure 6.1: Images taken of a lightning flash in Tuscon USA in 2007 for two different
perspectives approximately 34◦ apart. (a) Camera S1 (b) Camera S2.
A lightning flash was recorded in high speed video from two different perspectives
in Tuscon, USA [43]. The cameras were placed at approximately 34◦ angular
separation. A sample of the two images from the videos are provided in Figure 6.1a
and b. It should be noted that there are significant resolution disparities in the
two images (discussed briefly in Section 4.4.1), which would reflect in the model
resolution.
Chapter 6 — Physical Lightning Investigation 75
6.2.2 Reconstruction Results
The original lightning images in Figure 6.1a and b were processed to produce Boolean
images. These images were used to reconstruct a 3D model of the lightning discharge
channel, as shown in Figure 6.1. For Camera S1 perspective, the Boolean image and
corresponding model image – referenced at 0◦ – is provided in Figure 6.2a and b.
For Camera S2 perspective, the Boolean and model image – referenced at 34◦ – is
provided in Figure 6.2c and d.
(a) (b) (c) (d)
Figure 6.2: Reconstructed model of a single channelled lightning flash. (a) Cam-
era S1: Boolean image (b) Camera S1: Reconstructed image (c) Camera S2: Boolean
image (d) Camera S2: Reconstructed image.
6.2.3 Discussion
It is evident through visual comparison that the reconstructed model correctly
follows the path of the lightning channel in the images. In Figure 6.2b and d, several
segments are missing along the path of the reconstructed channel. These missing
segements correspond to the thinner areas of the channel, which demonstrates how
the reconstruction method fails when the channel is less than three pixels in width.
This has been a common observation from previous tests, and is explained by the
fact that normals may not be generated if a channel is one pixel or two pixels wide.
The reconstructed model has evident resolution errors, which is indicated in Fig-
ures 6.3 and 6.4. This set of images shows the propagation of errors in the re-
construction process in a direct comparison of each stage. The particular area of
interest, which clearly illustrates this error is highlighted in Figure 6.3. This segment
Chapter 6 — Physical Lightning Investigation 76
Figure 6.3: Original image from Camera S1 perspective indicating area of interest
for demonstrating errors in resolution in the reconstructed model.
(a) (b) (c)
Figure 6.4: Zoomed in area of interest showing resolution errors on the reconstructed
lightning model from Camera S1 perspective. (a) Original image (b) Boolean image
(c) Corresponding image of reconstructed model.
is chosen for its clear variation in channel definition in the original image. The
original image, Boolean image and corresponding model image reflecting the area of
interest is presented in Figure 6.4a–c.
It can be seen from a comparison of Figure 6.4a with Figure 6.4b that the digital
filtering stage already introduces minor errors in the definition of the channel
information. These errors may not be significant, but has a direct effect to the
quality of the model that is reconstructed, as the Boolean image is the only input
defined to the modelling stage.
A comparison of Figure 6.4b with Figure 6.4c demonstrates the resolution errors that
Chapter 6 — Physical Lightning Investigation 77
are subsequently introduced to the reconstructed model. It should be noted that the
thickness of the channel is determined by an averaging of radii of verified channel
segments, and therefore producing additional width errors if compared to the original
image from Camera S1 perspective. Due to the cruder resolution of the original
image from Camera S2 perspective, the resulting resolution of the reconstructed
channel of the model is bulkier and less defined. If different camera resolutions are
used to record the same lightning flash, these resolutions should be a contributing
factor in the camera placements.
6.3 Experiment B-2: Multiple Channels (South Dakota)
In this investigation, an upward lightning discharge channel with multiple branches
is reconstructed using images taken from Mr. Warner in 2010 [44]. Five cameras
captured the discharge channel from four different positions. The flash consists of
two significant parts: upward branching leaders from the tower tip, and a return
stroke extended across the horizon. Figure 6.5a presents the photographed image
of the branched upward leader channels for Camera W1, which will be the focus of
this investigation. The return stroke for this flash is presented in Figure 6.5b for
the same camera perspective. It should be noted that these two frames have been
selected from several frames illustrating the time resolved propagation of the flash.
(a) (b)
Figure 6.5: Camera W1 perspective of upward lightning leader propagation of
a branched flash photographed at multiple perspectives. (a) Multiple channels
(b) Return stroke.
Chapter 6 — Physical Lightning Investigation 78
6.3.1 Experimental Setup
Five cameras participated in the photography of an upward flash from the South
Dakota tower occurring in 2010. The locations of the camera setup, relative eleva-
tions and radial distances are presented in Table 6.1. All the cameras are located on
lower ground in relation to the tower position, which is demonstrated by a negative
relative elevation value.
(a) (b)
(c) (d)
Figure 6.6: Upward lightning leader propagation of a branched flash photographed
from Camera W2 to Camera W5. (a) Camera W2 (b) Camera W3 (c) Camera W4
(d) Camera W5.
The multiple perspectives on the upward branched leader propagation are presented
in Figure 6.6. It can be seen that Camera W2 and Camera W3 have little or no
distortion on the image, whereas Camera W4 and Camera W5 were photographed
with fisheye lenses and therefore contain a large amount of distortion. The lightning
discharge captured in Camera W5 is much clearer than the photographed image in
Camera 4 due to its closer proximity to the towers.
Chapter 6 — Physical Lightning Investigation 79
Table 6.1: Geographic information of cameras in relation to a flash photographed
on a tower in South Dakota.
Location Relative Radial
Reference Co-ordinates Elevation (m) Distance (km)
Tower 44.0687◦N 103.2514◦W − −
Camera W1 44.0324◦N 103.2728◦W −271 4.40
Camera W2 44.0336◦N 103.2857◦W −152 4.77
Camera W3 44.0348◦N 103.2880◦W −146 4.78
Camera W4 44.0348◦N 103.2880◦W −146 4.78
Camera W5 44.0615◦N 103.2501◦W −186 0.80
Table 6.2: Configurations for cameras participating in the photography of the flash
occurring on the South Dakota tower.
Camera Lateral Camera Image
Reference Separation Lens Distortion)
Camera W1 0◦ f/1.3, 3 mm -
Camera W2 12◦ f/1.4, 2.8 mm minor
Camera W3 15◦ – -
Camera W4 15◦ fisheye 1.4 mm significant
Camera W5 330◦ fisheye 1.4 mm significant
For reconstruction, Camera W1 is used as the reference camera, as its image provides
the clearest resolution and the most information on the lightning discharge, as shown
in Figure 6.5. The lateral separation of the remaining cameras are measured in
relation to Camera W1, and presented in Table 6.2. This table also presents the
specific camera information based on lenses used on the cameras and identifying any
significant image distortion which requires normalisation on the lens curvature.
Chapter 6 — Physical Lightning Investigation 80
6.3.2 Reconstruction Consideration
Since only three images are required for branched reconstructions, images from
Camera W1, Camera W2 and Camera W3 are used in the reconstruction. Due to
the major fisheye lens distortion on channel information captured from Camera W4
and Camera W5, the corresponding images are omitted from the reconstruction in
this investigation.
The three images participating in the reconstruction of the branched channel present
different portions of the channel in the captured frame. This is corrected digitally
to ensure that all the images include channel information that is mutually inclusive.
The comparison is performed by a crude matching of channel shape. This matching
method is unique to this case, because images are close in angular separation (i.e.
12◦ and 15◦ in relation to Camera W1 at 0◦), and no significant change is observed
in the channel shape from all perspectives.
Due to the acute angular separation on the three images, the variance of the channel
information is limited. This fact may produce inaccurate reconstructed models, as
the three-image algorithm was not designed for such small angular separations. To
evaluate the capabilities of the algorithm (for the use of two and three images)
efficiently, three tests are performed on the image data:
• Part 1: Fully Branched Channel
• Part 2: Simplified Branched Channel
• Part 3: Single Branched Channel
6.3.3 Reconstruction Results: Part 1
The fully branched lightning channel is reconstructed to test the capability of the
reconstruction algorithm for branched discharge channels. In particular, this set of
images tests the algorithm under the condition of acute angular separation of the
input images.
The filtered Boolean images of the three perspectives are provided in Figure 6.7.
The resulting images illustrating the reconstruction of the three-image model for
the two branched-channel is presented in Figure 6.8.
Chapter 6 — Physical Lightning Investigation 81
(a) (b) (c)
Figure 6.7: Fully branched channel Boolean images of upward flash return stroke;
cropped to include mutually inclusive data of the channel (a) Camera W1 at 0◦
(b) Camera W2 at 12◦ (c) Camera W3 at 15◦.
(a) (b) (c)
(d)
Figure 6.8: Reconstructed lightning channel of the fully branched channel of
the upward flash return stroke using two images (a) Reconstructed perspective
of Camera W1 (b) Reconstructed perspective of Camera W2 (c) Reconstructed
perspective of Camera W3 (d) Triple duplication of a channel.
Chapter 6 — Physical Lightning Investigation 82
It is difficult to discern any useful information from the images taken from corre-
sponding angles of the input images in Figure 6.8 (a-c). Despite this, it can be seen
that there are channel thicknesses much greater than the original channel widths
depicted in the input images. Additionally, it can be seen that redundant channels
are also reconstructed.
To investigate this reconstruction in greater detail, a different perspective is high-
lighted, in the form of Figure 6.8 (d). This image demonstrates the existance of an
offset occurring in the placement of the images, which produces three individual
channels that appear to follow a similar channel shape. This implies that the
images are not correctly aligned, and therefore reconstructs a ”ghosting” effect on
the channels.
6.3.4 Reconstruction Results: Part 2
The lightning branching information is simplified to the usage of only two branches
for reconstruction. This should provide the basic test for branched channel recon-
struction using the three-image reconstruction algorithm.
(a) (b) (c)
Figure 6.9: Two-branched channel Boolean images of upward flash return stroke;
cropped to include mutually inclusive data of the channel (a) Camera W1 at 0◦
(b) Camera W2 at 12◦ (c) Camera W3 at 15◦.
The filtered Boolean images of the three perspectives are provided in Figure 6.9.
The resulting images illustrating the reconstruction of the three-image model for
the two branched-channel is presented in Figure 6.10.
Chapter 6 — Physical Lightning Investigation 83
(a) (b) (c)
(d)
Figure 6.10: Reconstructed lightning channel of the two-branched channel of
the upward flash return stroke using two images (a) Reconstructed perspective
of Camera W1 (b) Reconstructed perspective of Camera W2 (c) Reconstructed
perspective of Camera W3 (d) Extent of the full model.
6.3.5 Reconstruction Results: Part 3
A single channelled discharge for the flash is investigated in the form of the return
stroke occurring for the tower flash. This provides the simplest form of reconstruc-
tion on a concept that has already shown to be sucessful. The difference is using three
images for the reconstruction, and the acute angle at which images are obtained.
The filtered Boolean images of the three perspectives are provided in Figure 6.11.
Two reconstructions are performed for this test, three-image and two-image recon-
structions. This allows for the comparison in the performance of the two different
algorithms on the same set of data at small angles of separation. The resulting
images illustrating the reconstruction of the two-image model is presented in Fig-
ure 6.12 and the three-image model is presented in Figure 6.13.
The two-image reconstruction demonstrates a model that correctly follows the path
of the channel — as expected. The significant observation from this model is the
Chapter 6 — Physical Lightning Investigation 84
(a) (b) (c)
Figure 6.11: Single branched channel Boolean images of upward flash return stroke;
cropped to include mutually inclusive data of the channel (a) Camera W1 at 0◦
(b) Camera W2 at 12◦ (c) Camera W3 at 15◦.
(a) (b)
Figure 6.12: Reconstructed lightning channel of the single branched channel of
the upward flash return stroke using two images (a) Reconstructed perspective of
Camera W1 (b) Reconstructed perspective of Camera W3.
greater relative thickness of the channel in comparison to the thickness of the original
images, therefore, producing disproportionately thick channel segments.
The three-image reconstruction appears to include a large amount of unwanted
information, particularly at the top and bottom of the channel. Closer observation
of this model reveals that redundant channel segments are included in the model;
i.e. the y-axis does not present unique channel information and therefore appearing
to form branching. It is expected that this is partially due to alignment of the three
images.
Chapter 6 — Physical Lightning Investigation 85
(a) (b) (c)
Figure 6.13: Reconstructed lightning channel of the single branched channel of
the upward flash return stroke using three images (a) Reconstructed perspective
of Camera W1 (b) Reconstructed perspective of Camera W2 (c) Reconstructed
perspective of Camera W3.
6.3.6 Discussion
The reconstruction of this particular set of images has tested the reconstruction of
discharge channels using images taken at acute angles more than the capabilities of
the reconstruction algorithm for branching channels. It has been shown that such
acute angular separation on the input images greatly distorts the channel that is
reconstructed. Despite the fact that models could not be correctly reconstructed,
some conclusions can still be made regarding the reconstruction of multiple channels
and reconstructions from input images from very acute angular separations.
Reconstructed Channel Thickness
The reconstruction of this discharge channel has produced models that have branches
of the channel that appear much thicker than the original image portrays. This
is expected according to the reconstruction algorithm; the radius of each channel
segment is determined by the intersections of outer normals of the white segments in
the image. At acute angles, the positions of the outer intersection points would occur
far from the center of the channel segment. This is demonstrated in an example of
images placed at 10◦ separation shown in Figure 6.14.
Chapter 6 — Physical Lightning Investigation 86
Figure 6.14: Channel thickness distortion modelled in the reconstruction due to
acute angles.
Duplicated Branches Reconstructed in Incorrect Positions
It is evident in the images of the models reconstructed that there are several
additional branches that are reconstructed, and should not appear in the channel.
This is clearly evident in Figure 6.8d and Figure 6.10d. This is likely due to
a problem with proper alignment of the images coupled with the extreme acute
angle of the input images. The algorithm for three-image reconstruction is designed
on a verification of cylinders, and because cylinders are so large in radius due to
the extreme acute angles, incorrect data is being incorrectly verified as a channel
segment. This is illustrated in the series of images in Figure 6.15a–c demonstrating
each step of the verification process.
Additional Image Information
The use of these images from Camera W4 and Camera W5 would provide addi-
tional channel information for future reconstructions and verification of channel
reconstructions. In particular the use of Camera W5 would provide a marginally
greater angular separation for the reconstruction, which could possibly provide a
better reconstructed model, if image correction can be sufficiently achieved. The
use of these two images would require significant image correction, of which open
source applications do not provide functionality for this type of fisheye lens.
Since Camera W3 and Camera W4 are placed in the same position, the image
correction of Camera W4 can be matched with the image provided by Camera W3
to provide a level of accuracy. Camera W4 and Camera W5 use the same fisheye
Chapter 6 — Physical Lightning Investigation 87
(a)
(b)
(c)
Figure 6.15: Verification process for redundant channels at acute angles. (a) Identi-
fication of cylinder centers and respective points (marked with ’x’) to calculate radii
(b) Virtual cylinders with radii determined by the averaged distances of ‘x’ points
(c) Third image verification incorrectly identifying all cylinders as valid.
Chapter 6 — Physical Lightning Investigation 88
lens, so given an appropriate match of Camera W3 and Camera W4 images due
to corrections, the same image correction can theoretically be applied to the image
from Camera W5.
6.4 Conclusion
The reconstruction of lightning discharge channels have provided similar results
to the reconstructed channels from the HV laboratory environment. These re-
constructions have demonstrated similar errors to the HV laboratory models, such
as missing segments and branch duplication. This shows that reconstructions are
mostly dependant on the quality of the input Boolean images, showing that the pre-
processing steps are a vital part to obtaining success reconstructions. Despite the
fact that reconstructed channels look similar to those produced from HV discharge
channels, there has been no verification performed on the two sets of images.
It has been shown that the model resolution is only as good as its weakest image
resolution. This should be noted for when camera resolutions are vastly differ-
ent, or if camera positions relative to the lightning flash differ significantly. It
is recommended that if multiple camera resolutions are used to photograph the
same discharge channel, that cameras with weaker resolutions be used in the closest
possible site.
Additional conclusions have been made, regarding the use of acute image per-
spectives. In this investigation, it has been shown that not only do the acute
angular separation of less than 15◦ produce thicker channel segments for single and
multiple branched channels. This is demonstrated in Figure 6.14. In addition to
the branched channel scenario, duplicated ‘ghosting’ channels are produced due to
incorrect validation of the channel segments. This is demonstrated in Figure 6.15.
This chapter has highlighted some difficulties that become evident in the large scale
lightning investigation into reconstructing the channels in 3D, and also presented
some of the limitations in the design of the reconstruction algorithms. The following
chapter discusses the comparison of the HV laboratory investigation and the physical
lightning investigation. Future extension to this study is also provided.
89
Chapter 7
Discussion and Future Work
In this chapter, the results of the laboratory investigation are compared
with the results from the physical lightning investigation. The system
is evaluated in its modular components through the results and future
reommendations in the refinement of each component are made.
7.1 Summary
The feasibility of reconstructing discharge channels from digital images is based
on evidence collected from several different sources, and the actual reconstruction
is based entirely on the reconstruction procedure discussed in Chapter 4. This
feasibility study therefore discusses the results of the investigation based on the
system mentioned herein and possible extensions to the project.
Table 7.1 provides a general summary of all the experiments discussed in Chapters 5
and 6 that have been performed for the feasibility study. The conclusion made for
each experiment is provided in the table, including the channel shape, number of
image inputs, angular separation of the cameras. For the channel shape option, S
denotes single-channelled discharges, and B denotes branched. The conclusions made
for each experiment provides the trend of whether datasets produced correct channel
paths, and if the model reconstruction has been verified through an additional
comparison. Each scenario is discussed further in this chapter.
Chapter 7 — Discussion and Future Work 90
Table 7.1: Summary of all experiments performed for reconstruction of discharge
channels under various algorithm configurations.
Experiment Channel Image Angular Correct
No. Shape (S/B) Inputs Separation Path? Verified?
A1 S/B 2− 3 Various True True
A2 S 2 120◦ True True
A3 B 2 45◦ False True
A3 B 3 45◦ True True
Appendix F B 1 – True –
B1 S 2 34◦ True –
B2 B 3 0◦, 12◦, 15◦ False –
B2 S 2 0◦, 15◦ True –
B2 S 3 0◦, 12◦, 15◦ False –
7.2 Single-Channelled Investigation
The reconstruction of single-channelled discharges is best suited with the use of
the two-image reconstruction algorithm discussed in Section 4.4.2. The three-image
reconstruction algorithm may also be used in the single-channelled discharge investi-
gation, but has shown to produce duplicated channels and occasionally discontinuous
channels.
The reconstruction of single-channelled discharges have been shown to be reproduce
the general shape of the discharge channel path through visual matching with
original images. This is determined by overlaying the reconstructed model over
the original image at its respective camera perspective. It has been noted that
possible inaccuracies may be based on resolution, lens curvature, and camera tilt.
7.2.1 Laboratory Discharges
Using a small-scale investigation of HV discharge channels, the reconstruction of
single-channelled discharges have shown to reproduce channel paths that generally
match in shape and size. The averaging option produces channels that visually
Chapter 7 — Discussion and Future Work 91
follow the general path, but may not necessarily provide an accurate reproduction
of the original channel path. The use of the first detect option provides good channel
continuation, whereby minimal missing channel segments are reconstructed, but also
produce more significant meshed branching duplication.
From Figure 5.4, two images are used to reconstruct a single channelled laboratory
discharge. Three cameras recorded the discharge at an angular separation of 120◦.
The image displaying the most channel curvature was omitted from the reconstruc-
tion. The reconstructed model produced similar curvature to the omitted image,
and on comparison, it is shown that a tilting factor separates the mismatching to
the original image. This type of verification has produced confidence in the basic
two-image reconstruction algorithm.
7.2.2 Lightning Discharges
From the physical investigation on two single-channelled lightning flashes in Tuscon,
it can be seen that the reconstructed channels match well with the original images
from the photographed perspective. This investigation demonstrated the limitations
in model resolution due to one image perspective lacking relevant channel detail.
It should be noted that if different camera resolutions will be used in a setup,
cameras with weaker resolutions are recommended to be placed closer to the intended
termination point. There were only two perspectives photographed for this lightning
event, and no additional perspective could provide verification on the larger scaled
reconstruction.
In addition, the return stroke of a flash from South Dakota taken at very acute
camera angles (≤ 15◦) has also been investigated. The two-image reconstruction
algorithm produces channels that follow the general path, but constructs channel
widths that are much thicker than expected from the original images at very acute
image angles. This is due to the thickness of each cylinder segment is dependant
on the intersections of each white-pixel segment extended from the original image,
and at very acute angles, the intersection points are much further away from the
cylinder centers, resulting in exaggerated radii. The three-image reconstruction
algorithm produces disproportionately thick channel segments, but still follows the
general path of the discharge channel shape.
Chapter 7 — Discussion and Future Work 92
7.2.3 Discussion
Two-image reconstructions cannot be readily verified if there is no additional per-
spective to provide comparison on the reconstructed model. If only two images
are recorded of a discharge channel, the only conclusion that can be made is that
recontructed segments match the path and thickness of the original image at the
given camera perspective at both perspectives.
The availability of three or more camera perspectives allows for the verification of
the two-image reconstruction algorithm. This has been verified in a controlled small-
scale environment, but the larger scaled environment investigating lightning flashes
has not yet provided verfication.
Three camera perspectives can also provide verification on the three-image algo-
rithm, although additional errors may be introduced to the model, such as missing
channel segments and duplicated channel segments, which are both indications of
slightly mis-aligned input images.
7.3 Multiple-Channelled Investigation
The reconstruction of multiple-channelled discharge channels is shown to generally
follow the channel path. As the three-image reconstruction algorithm stands, incon-
sistencies are introduced to the reconstructed channel through attempting to equally
use all the image information.
7.3.1 Laboratory Discharges
The laboratory investigation produced one branched discharge channel with cameras
placed at 45◦ separations. The channel has a single split, which provided the simplest
evaluation of the reconstruction algorithm. The reconstructed channel demonstrates
two known limitations of the three-image reconstruction algorithm: resolved channel
segment inconsistencies and missing channel segments.
Chapter 7 — Discussion and Future Work 93
7.3.2 Lightning Discharges
The physical lightning investigation has also produced one event of a multiple-
branched upward discharge channel photographed from five different perspectives,
taken from South Dakota. Two camera perspectives are omitted from the investiga-
tion due to significant image distortion from the fisheye lenses used. The remaining
three cameras recording the event are placed in very acute angles of≤ 15◦ seperation.
The reconstruction of multiple channels with images taken from the very acute angles
provided general channel paths, but included errors such as redundant channels and
disproportionately thick channel segments. These errors have been found to be
caused by the design of the reconstruction algorithm.
Reconstructing branched discharge channels using one branched image perspective
provides a proof-of-concept for more complex branched channels. This tests the
scenario for 90◦ camera separations where one image provides no branching informa-
tion. This investigation does not resolve any 3D channel information, but accurately
reconstructs the branched channel using the three-image reconstruction algorithm.
It is shown from this investigation that the algorithm fails for very thin channels i.e.
one or two pixels in width.
7.3.3 Discussion
Multiple-channelled discharge reconstructions are successful under ideal conditions;
i.e. 90◦ angular separation (with no 3D definition) and 45◦ separation in the
laboratory environment. The best algorithm configuration for resolving channel
branching for one double branched channel is Case 004. The algorithm fails in the
reconstruction of multiple channels at very acute angles ≤ 15◦, by reconstructing
redundant channels and producing channel widths that are much thicker than
portrayed in the original images.
It is important to use three input images for branched channels. Despite the fact
that two-image reconstructions using the first detect option can provide acceptable
models, it is hard to determine whether the resolved channel branches are correctly
modelled, or if the ambiguities have been resolved instead. There is a 25% chance
of the branches being correctly placed. A third image is imperative in providing
the channel segment validation, and eliminating the ambiguity branched channels
present.
Chapter 7 — Discussion and Future Work 94
7.4 System Evaluation
This investigation has shown that the system still has several flaws; and due to
these flaws, has resulted in imperfect discharge channel reconstructions. Despite the
errors observed, the weaknesses of the system are known, and as a proof of concept,
the system has been shown to be successful in reconstructing discharge channels,
with confidence gained in its single-channelled reconstructions. The known system
flaws are discussed and critiqued in this section, leading up to a plan to extend this
current work and the system capabilities.
7.4.1 Reconstruction Framework
The reconstruction framework refers to the process involved after image processing,
and before the reconstruction algorithm is applied. This framework determines the
virtual environment for reconstruction, which deals with the image placement with
respect to the origin of the environment. This part of the system has not been
directly tested in the scope of this study, but through the investigations in this
study, some future modifications have been identified to provide more optimised
channel reconstructions. This may include providing feedback functionality to the
placement of images in the virtual environment, to produce optimised models with
minimal missing segments and reduce channel duplication.
7.4.2 Image Pre-Processing
The filtering of images to the Boolean images used as inputs for the reconstruction
algorithm has shown a successful elimination of redundant image information, and
the successful identification of relevant discharge channel information.
Nonetheless, this investigation has identified the need to normalise images according
to camera tilt or camera lens curvature. An additional pre-processing step on the
images can be incorporated to resolve this problem and assist in producing more
accurate models.
Chapter 7 — Discussion and Future Work 95
7.4.3 Reconstruction Algorithms
The general method in reconstructing discharge channels using stacked cylinder
segments has been shown to be a simple method of tackling a complex 3D problem.
Common faults found in general method used in the reconstruction algorithms
have shown to produce missing channel segments (most notably demonstrated by
Figures 5.7 and 6.2) and disproportionate channel widths at acute image perspectives
(as demonstrated in Figure 6.14).
Missing channel segments have been found to result from input image data with
channel sections of less than 3 pixels in width. If channel sections are not at least
3 pixels wide, a center, left and right normal cannot be extended from the relevant
white pixels, resulting in a null channel segment and a discontinuity in reconstructed
model. Future modifications would have to either limit the system from accepting
channel widths less than 3 pixels in width, or would need to account for these narrow
channel portions.
Disproportionate channel widths appearing in the reconstructed model are a result
of the method in which the channel segment radii are calculated. This method was
originally designed for angles of separation of over 30◦. It was assumed at the time
that camera perspectives smaller than that would not provide sufficient 3D spatial
information significant enough to reconstruct a model. The channel segment radius
is calculated from the intersection of a center normal of a white channel section in
one image with a left or right normal of a corresponding white seciton in another
image from a different perspective. This dynamic radius is dependant on the angle
of separation on the input image perspectives, which does not make logical sense
and should be revised.
Future modifications made to this algorithm would include the calculation of channel
segment radii independant of the image angular separation, and only based on the
width of the white sections of the input images. This means that diameters will
be calculated as an average of corresponding channel widths in the 1-pixel high
sections. If intersections of far left and right normals with center normals are no
longer required in the algorithm, this could reduce the number of required normals
per 1-pixel high which image section to only one center normal. The application
of this would also solve problem concerning missing channel segments due to thin
channel widths.
Chapter 7 — Discussion and Future Work 96
Two-Image Reconstruction Algorithm
The two-image reconstruction algorithm has been validated in its ability to correctly
reconstruct a discharge channel given only two perspectives (as shown in Figure 5.5).
A valid model has been verified using a comparison with a third perspective that has
not been used in the system as an input to the recontruction. The resulting model
demonstrates a slight tilt in a portion of the reconstructed channel, but this offset is
a result of the image alignment, and not the fault of the reconstruction algorithm.
Three-Image Reconstruction Algorithm
The reconstruction algorithm for three-image inputs have shown to produce redun-
dant channel segments, sometimes meshed about a similar axis (as demonstrated in
Figure 5.9), or extended far from the model center (as demonstrated in Figure 6.10d).
Duplicated channel meshing provides an indication that images are not properly
aligned, and therefore slight offsets occur in the calculated cylinder segment centers.
The meshed channel branches can be solved by a re-evaluation of the verification
method for channel segments, and can probably be optimised in the positioning of
the images providing the best fit for the channel. However, this is out of the scope
of this investigation. Occasionally, missing segments may also present the same
indication.
An acute angular separation of the image perspectives produces redundant channel
branches extended far from the model center, as demonstrated in Figure 6.15.
A possible modification to the reconstruction algorithm has been provided for
preventing the reconstruction of these redundant channels in Section 7.4.3.
7.4.4 Testing Model Accuracy
Currently, the most useful method of testing the accuracy of the reconstructed
models is through a visual comparison of the Boolean image and the image of the
matching model perspective. The visual comparison comprises of an evaluation
of a matching channel shape, segment continuity and whether signficant channel
duplication is reconstructed. These evaluations are performed using a side-by-side
comparison of the Boolean image and the image of the reconstructed model at the
same perspective.
Chapter 7 — Discussion and Future Work 97
The testing framework currently provides two automated evaluations: the percent-
age mismatch between the two images, and the percentage error of total white
pixels reconstructed from a perspective matching. Both calculations provide a vague
indication of the reconstructed model perspective, and little conclusion can be made
with the results of each calculation.
Future improvements to the testing framework could provide better functionality to
the automated testing of the image datasets through image processing. This would
reduce evaluation times and provide a more accurate description of the reconstructed
models. This could be achieved in two ways:
1. Direct pixel matching of the two images and,
2. Idenfication of pixel coordinates demonstrating branching of branch tips and
matching coordinates of both images.
Additionally, models can be compared using the reconstructed coordinates of the
channel segments, which may include the position of the segment center and the
calculated radius. This test would only be able to be performed on models recon-
structed from the same set of data, such as a comparison between the algorithm
configurations, Cases 001− 007.
7.4.5 Future Work on Image Data
A future objective of the work regarding this project is the collection of multiple
lightning perspectives with the camera setup in Johannesburg, either on Brixton
tower or Hillbrow tower. The collection of this image data would be more stringently
monitored and will provide wider angular separation on image datasets than was
provided from South Dakota as discussed in Section 6.3.
In Johannesburg, there are two cameras are currently monitoring Brixton tower,
one camera monitoring Hillbrow tower and another camera monitoring the Johan-
nesburg skyline. The lightning incidence of the towers in question are discussed in
Section 2.3.2. For the purpose of future 3D lightning reconstructions, the Brixton
tower setup is discussed in this section.
Camera locations in relation to Brixton tower are provided in Table 7.2, and pro-
duced graphically in Figure 7.1. Observation of Brixton tower has been operational
Chapter 7 — Discussion and Future Work 98
Table 7.2: Geographic information for Brixton tower and the relative camera
locations.
Location Co-ordinates Elevation (m) Distance (km)
Brixton Tower 26◦11′33′′S 28◦00′25′′E 1779 –
Site 1 26◦11′29′′S 28◦01′32′′E 1714 1.88
Site 2 26◦11′10′′S 28◦00′30′′E 1739 0.71
Figure 7.1: Camera views on Brixton tower indicating an approximate 70◦ separation
between the two sites.
since November 2009 from Site 1. The camera was set up to face Brixton tower from
an observation point at the University of the Witwatersrand. The physical distance
between the location of the tower and the observation site is approximately 1.88 km.
Observation at Site 2 includes a portable setup using an Axis P1344. No image
sets have been recorded from Site 2 due to difficulties in remote monitoring and the
overall statistical nature of lightning to tall structures, as highlighed in Section 2.2.1.
The collection of such image data is expected to be a long-term goal of this project.
The collection of image data in this setup will provide testing information for
different camera elevations, as shown in Figure 7.2. An elevation normalisation
on the images would need to be implemented and properly tested for this scenario.
Chapter 7 — Discussion and Future Work 99
Figure 7.2: Two camera sites providing vastly different camera elevations observing
Brixton tower.
This would also open up the scope of channels that can be photographed with
the current equipment, including the possible 3D reconstruction of rocket-triggered
lightning channels – currently an ongoing project performed by the research group.
Additionally, more lightning images from different perspectives will be collected
from multiple sources to start building up a database of lightning channels. With
current camera technology, lightning channels are being recorded in high-speed,
which provides a time resolution of leader propagations. If this information can
be captured from favourable angular separations, this could open up a scope for
time-resolved lightning channels.
The following chapter summarises the findings of this work, in regard to the evalu-
ation of the system and the two discharge environment investigations.
100
Chapter 8
Conclusion
A system has been introduced and described for producing images capable of recon-
structing 3D models of discharge channels. Each component of the system is modular
and can be refined without difficulty. The system capabilities and limitations have
been evaluated through the investigation of HV laboratory discharges, and full scale
lightning discharges. Each discharge environment has produced at least one sample
of single-channelled and multiple channelled discharges, which are used to evaluate
both two- and three-image reconstruction algorithms.
It can be seen that results from the laboratory and natural lightning investigations
are similar; showing the relevance of conducting small scale tests to determine
preliminary results for channel reconstruction. Several fundamental conclusions can
be made using small-scale reconstructions of discharge channels. This includes the
performance of all the algorithm configurations involved with two- and three-image
reconstructions. From small scale investigations, the best algorithm configurations
can be determined for use in lightning channel reconstructions, once images have
been obtained. In addition, verification has been performed on the two-image
reconstruction algorithm, which provides confidence in the reconstructed models,
provided that input images are set according to the angular specifications.
The reconstruction of lightning channels obtained from different sources has provided
an acceptable proof-of-concept. Although, the image datasets have also indicated the
limitations in the current reconstruction algorithms. The reconstruction of complex
lightning channels with multiple branches cannot be fully evaluated, due to the
limited image data set. Nonetheless, acceptable models have been reconstructed for
a two-branched laboratory channel.
Additional work needs to be performed on the system to provide more accurate
Chapter 8 — Conclusion 101
and comprehensive models. This includes the addition of an image pre-processing
step to provide sufficient normalisation for camera elevation, tilt and lens curvature.
This also includes tweaking the reconstruction algorithm such that channel widths in
images less than three pixels wide can be properly reconstructed without producing
missing segments. The algorithm also needs to be changed to produce channel
segments that are not dependant on the angle of separation, as this has shown to
provide inaccurate models in the form of thicker channel segments and duplicated
branches. Testing models through visual evaluation has provided some insight, but
is largely subjective. Direct pixel comparisons need to be made on the Boolean and
model images to produce proper matching of channel data.
Although natural lightning investigations have been assessed using image data taken
from different image sources, an evaluation on lightning images recorded from the
Johannesburg camera setup must still be performed as an extension to this project.
This is subject to the statistical nature of the lightning event to tall structures, and
the difficulties experienced from remote monitoring and placement of cameras.
102
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Appendix A
Discharge Channel Photography
A.1 Introduction
The photography of discharge channels is not trivial. This appendix provides a
summary of the camera technologies that can be used to photograph the fast
transient events. Furthermore, additional information is provided on the current
cameras available for this investigation.
A.2 Possible Camera Solutions
There are several capture devices and techniques available for capturing an image
of a lightning discharge channel. Five types of capture devices have been identified
as the more commonly used techniques at present time for photographing lightning
channels. This discussion will provide a brief comparison of each type.
• Converter camera and streak camera
• High-speed video camera
• Still-digital camera
• Digital video camera
• Analogue still camera
Converter and streak cameras are capable of measuring very fast phenomena such
as the propagation of the leader or return stroke [18]. With this in mind, they
Appendix A — Discharge Channel Photography 107
have insufficient recording time to measure entire discharge channel. High-speed
video cameras can optically observe an entire discharge, but is very expensive.
The advantage of using the high time resolution cameras is that the chance of
overexposure to the image sensor is very rare, as seen in image comparisons in [8].
The digital video camera can record entire flashes, although the time resolution
is not capable of distinguishing individual strokes. The analogue still camera is
capable of capturing fast phenomena by leaving the aperture open for long exposure,
which is useful for eliminating the problem of triggering the camera shutter. The
drawback with the still-analogue option occurs with overexposure of the film and the
need for processing the film before it could be properly analysed. The conventional
still/video cameras provide an affordable solution, although the image sensor has a
high possibility of being overexposed.
The other problems pertinent to photographing lightning are addressed with spe-
cial techniques. There are certain methods that help to eliminate the problems
mentioned with the photography of lightning. Over-exposure of the image sensor
caused by the intense light flooding the lens is solved by using optical filters, which is
significant in the absence of aperture control on the camera. The uncertainty of the
strike termination point is eliminated by focusing the camera to capture lightning
attachment on a tall structure. Another issue is the lack of certainty for when a
strike will occur. This problem can be addressed with the use of an electromagnetic
sensor or light sensor, which could be expected to trigger the capture device when
a strike is sensed.
A.3 Summary of Camera Settings
Chronologically, cameras of the Axis 207 range were obtained first (four 207W
and one 207MW). These cameras were originally chosen for its wireless property.
Through discovered limitations in these camears, discussed further in Section 4.2.4,
an Axis M1011 was obtained to replace damaged cameras. At the time, the 207 range
was discontinued, and the M1011 was the upgraded version. At a later stage, four
Axis P1344 cameras were obtained, which were considerably more expensive, but
have power options that are beneficial for use in high electromagnetic environments,
discussed in further in Section 4.2.4. These cameras also presented an indoor or
outdoor installation option, providing more flexibility in camera positioning.
Appendix A — Discharge Channel Photography 108
The usage of all the cameras discussed are summarised in Table A.1. The camera
capabilities provided for each camera type demonstrates the highest or maximum
setting. Some settings are variable and can be reduced to less complex specifications.
Table A.1: General camera settings configured for the laboratory and/or physical
investigation.
Camera Property 207W 207MW M1011 P1344
Relative Cost low moderate moderate high
Electrical Isolation − − − 12 battery
Quantity 4 1 1 4
Damaged 3 1 0 0
Currently Operational 1 0 1 4
Location 1 (L1) − 1 (L2) 1 (L3)
1 (L4)
2 variable
Resolution (pixels) 640× 480 1280× 1024 1024× 640 1280× 800
Frame-rate (fps ) 10− 15 10− 15 10− 15 30
Trigger motion motion motion motion
Pre-buffer (s) 2 2 2 2
Optical Zoom − − − yes
Set Colour Option greyscale greyscale greyscale variable
Image Slicing vertical vertical unknown pre-buffer
wireless/ wireless/
Communication LAN LAN LAN LAN
Storage Method FTP FTP FTP on-board
Storage Location directory directory directory SD card
File Format JPEG JPEG JPEG MKV
Data Conversion − − − MKV to JPEG
Appendix A — Discharge Channel Photography 109
A.4 Conclusion
This appendix provides some camera technology which can used in the photography
of discharge channels. This is not an all-inclusive list of technologies available.
Lastly, surveillance camera technologies used in this study have been provided.
110
Appendix B
Motivation for Three-Dimensional
Study of Lightning
B.1 Preamble
This appendix is a paper that was accepted and presented for publication by
the International Conference on Lightning Protection (ICLP) in 2010, hosted in
Cagliari, Sardinia. The paper is entitled: Observation of Lightning Discharges
on Brixton Tower .
B.2 Paper Description
This paper discusses general observations of lightning to Brixton Tower in Johan-
nesburg, and presents a photographed case of downward lightning appearing to
trigger upward lightning on a nearby tower. Lightning data from the South African
Lightning Detection Network (SALDN) is used to analyse the photographed events
through matching of the times and location data.
This investigation proved through the fact that only one camera perspective captured
this event, and therefore provides the scope and motivation for reconstructing 3D
models of lightning.
OBSERVATIONS OF LIGHTNING DISCHARGES ON BRIXTON TOWER
Y.C.J. Liu, H.G.P. Hunt, M.D. Grant and K.J. Nixon
University of the Witwatersrand, Johannesburg, South Africa
Yu-Chieh.Liu@students.wits.ac.za
ABSTRACT
Observations of lightning strikes to Brixton Tower in South
Africa are investigated in this paper. The tower is topograph-
ically situated in an ideal location to study lightning strikes,
and has the benefit of a physical height of 250 m. Observa-
tions presented in this paper were made through photographic
recordings of lightning events from November 2009 to May
2010. Lightning data from the Southern African Lightning
Detection Network (SALDN) is used to match recorded light-
ning strokes to photographed events. The SALDN provides
the associated stroke parameters for assessment of the events
in terms of peak current values as well as rise and decay times.
Particular focus is given to studying positive polarity events.
This includes an investigation into positive strikes to the tower
and an event of a downward positive flash that appears to ini-
tiate an upward flash from the tower.
1 INTRODUCTION
Lightning study observations of frequently struck
structures have formed an important component of
lightning research [1–4]. Since lightning has a tendency
to attach to the tallest object in its immediate area —
these structures are typically tall or isolated. Brixton
Tower (also known as Sentech Tower) is a structure that
stands 250 m tall in Johannesburg, South Africa [1].
It is an ideal site for observing lightning activity, due
to its elevated topographical location, physical height
and lower-rise buildings in the immediate vicinity. An
observation point was set up to photograph lightning
strikes to the structure. Several events are compared
to the corresponding lightning data from the South
African Lightning Detection Network (SALDN). Some
of these events, which feature mostly positive polarity
flashes, are presented and analysed in this paper.
2 BACKGROUND
Brixton Tower stands quite prominently as the
tallest structure in the immediate area. This topo-
graphical advantage prompted the setup of the surveil-
lance system to collect optical lightning data attaching
to the tower for a work involving the reconstruction of
three-dimensional models from photographs [5]. Light-
ning data from the SALDN is used to quantify current
parameters of the attaching lightning discharges to the
tower. Using both optical and SALDN data, motiva-
tion is presented for using Brixton Tower as a observa-
tion point for lightning events. This takes the form of
an investigation into the flash count of the tower, up-
ward vs. downward strikes, and positive vs. negative
polarity strikes.
2.1 Surveillance Considerations
A low-cost surveillance camera was set up to
face Brixton Tower from an observation point at the
University of the Witwatersrand. The local area
has a high ground flash density, Ng, of 7.5 – 12
flashes/km2/year [6, 7]. Photographs of the lightning
activity was triggered by motion detection. The cam-
era was situated indoors, behind a glass window, which
explains some blemishes in the frames and light distor-
tions due to rain droplets. An infrared filter was placed
over the camera lens to reduce the light intensity to the
image sensor.
The observation point was specifically set up for a
project that requires optical lightning data. Therefore,
no corresponding electromagnetic fields, or current val-
ues were measured for the associated lightning events
at the surveillance site. The surveillance camera used
has a frame-rate of 10 frames per second with the use
of a pre-buffer, essential for capturing the images [5].
This leaves a general time-resolution within the range
of 100±20 ms. Since only one perspective of the light-
ning event is photographed, most of the spatial distri-
bution of the events were limited to a two dimensions.
The reliability of the motion detection triggering is un-
known, and it is possible that some events may not
have been captured.
2.2 The Southern African Lightning Detection Net-
work (SALDN)
The SALDN is a lightning location system consist-
ing of 20 Vaisala LS7000 sensors (19 sensors in South
Africa and 1 located in Swaziland) [7, 8]. The light-
ning detection network was commissioned by the South
African Weather Service (SAWS) and has been opera-
1073-1
tional since January 2006.
At present, the South African system has not been
calibrated using ground-truth data. An early investi-
gation was performed into the ground stroke count of
the area around Brixton Tower using the historical data
from the SALDN presented in Figure 1. A ground flash
density of 20 flashes/km2/year is suggested, assuming
an average stroke number per flash of 2.5 [9]. This
preliminary study of the SALDN is subject to further
investigation.
Figure 1: Ground stroke count for Brixton Tower (and Hillbrow
Tower) area using SALDN data for 801 days of obser-
vation on an approximate 1 km2 grid.
In order to compare the SALDN data with the pho-
tographs, strokes reported by the SALDN need to be
matched to the photographs through timing and posi-
tion of known strikes. The preferred method of doing
this would be to compare times, however, since the
surveillance was not initially intended for comparison
purposes, it was not synchronised to a standard time.
It was noted that the camera clock was approximately
2:30 minutes off standard time. Consequently, absolute
time comparison is difficult.
However, as Figure 1 shows, a high density of
strokes occurs in the location of the Brixton Tower at
(26◦ 11’ 32.82” S, 28◦ 00’ 24.73” E) and Hillbrow Tower
at (26◦ 11’ 12.51” S 28◦ 02’ 57.66” E) — a nearby tower
4.8 km east north-east of Brixton. Clearly, the
SALDN is recording lightning strokes to the Brix-
ton Tower although there is a slight offset in the re-
ported location. Given this, the assumption is made
that strokes reported within this area and within
the approximate time of the correlating photographs
are, indeed, the photographed strikes. The identi-
fied strokes had a maximum latitudinal deviation of
26◦ 10’ 48” S to 26◦ 12’ 00” S and a longitudinal devia-
tion of 27◦ 57’ 00” E to 28◦ 01’ 30” E. The reported data
was examined for up to 5:00 minutes after the recorded
time of a photograph.
2.3 Preliminary Flash Count to the Tower
A flash count investigation from existing data will
serve as an indicator for the high lightning activity to
the tower. Using Eriksson’s empirically derived equa-
tion in Equation 1 [10], the expected annual light-
ning incidence, N , to the 250 m tall tower is 15 to 24
flashes/year.
N = 24× 10−6 ×H2.05s ×Ng (1)
where Hs is the height of the structure in m and Ng is
the ground flash density in flashes/km2/year. An effec-
tive height is recommended [2], but since the tower is
slender in comparison to its height, the physical height
is used. Using Equation 2 [11], the probability of up-
ward flashes occurring on Brixton Tower is 61.53%.
Pu = 52.8ln(Hs)− 230 (2)
The predicted flash count to the tower and upward
probability is compared to the observed incidence in
Table I.
Table. I. Flash Incidence to Brixton Tower.
Result Upward
(flashes/year) Probability
Eriksson 61.53%
Ng = 7.5 15 -
Ng = 12 24 -
Surveillance* 19 63.16%**
SALDN 20 -
* Lightning incidence for only 7 months of a year.
** 12 of 19 recorded flashes displayed upward branching, the
remaining flashes were inconclusive on the direction of propaga-
tion.
The surveillance has been operational for the bulk
of the 2009/2010 thunderstorm season in South Africa.
A total of 19 strikes to the Brixton Tower were recorded
by the surveillance, which falls between the two calcu-
lated flash densities of 15 to 24. Although the pre-
diction accounts for a year’s worth of data, the thun-
derstorm season is expected to provide the bulk of the
flashes to the tower since it includes a large portion of
the South African thunderstorm season. This shows
that the flash density has shown an increase since 7.5
flashes/km2/year was reported.
Of the 19 strikes to the tower, 14 could be con-
fidently identified from the SALDN data. Within this
1073-2
(a) (b)
Figure 2: Downward flash triggers upward flash from Brixton Tower (a) downward flash 16:29:33.850 (b) upward flash 16:29:33.970
dataset, 3 strikes were recorded with a positive polarity
(21.4%), and 11 were recorded with a negative polarity
(78.6%).
3 ANALYSIS OF SURVEILLANCE
The surveillance provides evidence of lightning
flashes to the tower. Two notable observations have
been made, which include an event in which a down-
ward flash triggers an upward flash, and an investiga-
tion into positive strikes observed.
3.1 Downward Triggers Upward
Figure 2 (a)-(b) presents what appears to be a
downward strike, which initiates the triggering of an
upward strike through the enhancement of the local
electric field. This data was taken during a short day-
time thunderstorm on 2009-11-02, 16:29.
3.1.1 Descending Flash Analysis
The first frame shown in Figure 2 (a) demonstrates
a highly charged channel from the cloud charge centre
in the left side of the frame to a structure behind the
Brixton Tower. The downward path does not seem very
tortuous although it has a minor branch directly behind
the tower. The attachment point of the main chan-
nel has a two-dimensional distance of 176.5 m from the
base of the tower, and 235.3 m from its minor branch
attachment. These distance values were obtained using
the a pixel-to-distance ratio using the tower height as
a reference.
A flash proceeded by a large amount of cloud activ-
ity, (mostly) single stroke flash, long horizontal chan-
nels and minimal branching are characteristics of pos-
itive lightning [12, 13]. This is further supported bythe SALDN, which recorded a positive stroke located
within the two-dimensional distance of the primary
channel from the downward flash in Figure 2 (a). The
detected stroke had a recorded return stroke of 16 kA
with a rise time of 10.6µs and a peak-to-zero time
of 14.2µs. It appears that the upward flash was not
recorded by the system.
Since the downward channel has been determined as
a positive flash, conventional attractive radius calcula-
tions do not apply to this situation. Petrov and Waters
formulated an expression to relate positive downward
stroke return current, Ip and height of the structure
to the striking distance (or attractive radius, Ra) [14].
Petrov and D’Alessandro later revised the expression to
accommodate structure heights greater than 200 m [15].
An attractive radius R+a of 28 m is determined for apositive peak current of 16 kA, which shows that there
is little possibility of the stroke leader intercepting any
upward leaders from the tower.
R+a = 0.103[(Hs + 30)Ip]2/3 (3)
Figure 3: Scaled overhead view of the downward positive flash de-
tected by the SALDN with respect to the surveillance
setup. a1−4: Downward flash indicators, b1: Brixton
Tower, c1: Charge centre indicator, O1: Surveillance
location.
1073-3
(a) (b)
Figure 4: Positive strikes to the tower as recorded by the surveillance (a) 2010-01-07 (b) 2010-04-20.
Figure 3 shows a graphical representation of the
analysis performed for the downward flash. The down-
ward stroke detected by the SALDN is marked by
a1 with an error ellipse around the point of detec-
tion. There lies a 50% probability that the stroke ap-
pears within the error ellipse. The downward stroke as
viewed by surveillance in Figure 2 (a) is represented
by the extended line from the camera at O1 through
a2 which is 176.5m south of the tower location. This
line intersects with the error ellipse at a3 and a4, which
provides a higher probability of the stroke termination
point location between the two points.
This criterion alone does not explicitly provide con-
clusions that the descending positive leader could not
intercept an ascending negative leader from the tower.
The path of the downward leader from a charge centre
in the clouds must be evaluated to confidently conclude
that attachment to the tower was not possible in this
situation. The charge activity in the clouds is assumed
to be the position of the charge center. This is marked
by c1 in Figure 3, using the high-rise building directly
below the charge centre as an indicator. A line is ex-
tended from the camera through c1 to provide a depth
perception lacking in the frame, which indicates the
possible locations of the charge center. Unfortunately,
further analysis cannot be performed due to the lack of
a second optical perspective. This illustrates the im-
portance of obtaining a three-dimensional perspective
of the lightning channel.
3.1.2 Ascending Flash Analysis
The second frame in Figure 2 (b) clearly demon-
strates a branched upward strike from the Brixton
Tower 120 ms later. This frame shows that the down-
ward strike is still illuminated. The upward leader is
assumed to be a negative leader for two reasons; charge
intensification will be negative at the tip of the tower,
induced by a positive stroke, and the upward stroke ap-
pears to be highly branched, which is a common char-
acteristic of negative leaders.
Most upward lightning assessments consider the
positive ascending leader scenario i.e. Rizk’s upward
leader inception criteria in [16–19], but do not consider
the negative ascending leader scenario. This assess-
ment cannot be taken further without knowledge of
the leader inception criteria for a negative leader. Fur-
thermore, the charge intensification of the tower cannot
be determined due to unknown initial conditions of the
tower tip before the downward stroke and due to the
unknown propagation of the downward channel path.
3.2 Observed Positive Strokes
Positive strikes are known to be less frequent than
their negative counterpart. There were a total of three
positive strokes recorded by the surveillance camera
with corresponding SALDN data. Stroke 2009-11-02 is
the downward positive stroke mentioned in Section 3.1,
the only stroke not attached to the tower. The remain-
ing two are presented in Figure 4, where (a) has com-
pletely overexposed the frame without any evidence
of branching (in any of the captured frames) and (b)
has evidence of upward branching. Each of the strikes
contain only one recorded stroke, as expected. The
SALDN data also records rise times (τ1) and peak-to-
zero times (τ2) for each detected stroke, as presented
in Table II.
Equations reproducing positive-polarity waveshape
curves have not been produced due to the limited num-
ber of recorded positive strokes [20]. Heidler’s func-
tion Equation 4 was implemented to produce the wave-
1073-4
shapes in Figure 5 for demonstrative purposes, even
though it was emperically derived for negative first
strokes [21].
Table. II. Parameters measured by the SALDN for observed
positive strokes to and around Brixton Tower.
Stroke Ip (kA) τ1 (µs) τ2 (µs) Q0(C)*
2009-11-02 16 10.6 14.2 3.6
2010-01-07 19 2.6 30.2 19.7
2010-04-20 7 9.8 15.6 2.4
* The charge value is estimated using Equation 6 and the pa-
rameters in Table II.
i0(t) = I0η
(
t
τ1
)n
(
1 + tτ1
)n exp
(−t
τ2
)
(4)
where
η = exp
(
−τ1
τ2
(nτ2
τ1
) 1
n
)
(5)
The drawback to using Equation 4 was that steep-
ness factor parameter n was varied in order to obtain
the correct peak current. By tending n to ∞ the cur-
rent peak tends to the measured current values, but the
front time becomes increasingly steep, with the wave-
form only rising approximately 10µs after it was ini-
tially meant to rise. For the strokes on 2009-11-02 and
2010-04-20, n=4 and 2010-01-07 n=30 to achieve the
correct peak current values.
0 10 20 30 40 50 600
2
4
6
8
10
12
14
16
18
20
Time (µs)
Cur
ren
t (kA
)
Positive Strokes
 
 
2009−11−02
2010−01−07
2010−04−20
Figure 5: Simulated waveforms of positive strokes using Equa-
tion 4 to and around Brixton Tower from parameters
in Table II.
Q0 =
(I0τ2
η
)∫ ∞
0
ξne−ξ
(τ1/τ2)n + ξn dξ (6)
where
ξ = t/τ2 (7)
It can be seen that 2010-01-07 has a large area un-
der the curve. By performing charge transfer calcula-
tions from Equation 6 shown in Table II [21], the charge
of this stroke appears to be significantly greater than
the other two strokes. This fact could account for the
overexposed frame in Figure 4 (a), despite its relatively
low current peak of 19 kA compared to the median peak
documented by Saba et al of 28 kA [13].
4 FUTURE WORK AND ANALYSIS
This work has been limited by using two-
dimensional spatial distribution. Work is currently in
progress to provide another perspective of the tower at
an approximate 90◦ separation. The additional view
point will provide the possibility for reconstructing a
three-dimensional channel of the flash.
A full analysis of the flash count of Brixton Tower
needs to be made after at least a year’s worth of in-
formation has been captured, which will provide a
more accurate indication of the relationship between
expected probabilities and recorded data. This may
provide an increased flash count, which would suggest
a higher ground flash density in Johannesburg.
At this stage is no instrumentation on the tower,
and therefore the SALDN provides the only measured
lightning parameters. Steps will be taken to provide in-
strumentation to correspond with the photographic im-
ages. Furthermore, the SALDN will be fully evaluated
in terms of detection efficiency and location accuracy
using ground-truth data in the future.
5 CONCLUSIONS
From the work presented in this paper, photo-
graphic records of lightning strikes to Brixton Tower
have relevance to general lightning assessments, includ-
ing upward vs. downward and positive polarity vs.
negative polarity analyses, and observations of unique
lightning events.
Although the SALDN has not been tested rigor-
ously against ground-truth data, it is evident that flash
densities are higher at high-rise towers (Brixton and
Hillbrow Towers). This provides confidence in using the
lightning data from the SALDN in these assessments,
particularly in the absence of measurements conducted
at the site.
This paper presents the limitations of using one op-
tical perspective, therefore providing scope for three-
dimensional reconstruction of lightning discharge chan-
nels.
1073-5
6 ACKNOWLEDGEMENTS
The authors would like to thank the South African
Weather Service (SAWS) for their support and for pro-
viding the SALDN data used in this paper. They would
also like to thank CBI-electric for funding the Chair of
Lightning at the University of the Witwatersrand and
for direct support of the Research Group. They would
also like to thank Eskom for the support of the Light-
ning/EMC Research Group through the TESP pro-
gramme. Thanks are extended to the department of
Trade and Industry (DTI) for THRIP funding as well
as to the National Research Foundation (NRF) for di-
rect funding of the Research Group.
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117
Appendix C
Ground-Work for System
C.1 Preamble
This appendix is a paper that was accepted and presented for publication by the
South African Universities’ Power Engineering Conference (SAUPEC) in 2009,
hosted in Stellenbosch, South Africa. The paper is entitled: Laboratory Inves-
tigation into Reconstructing a Three Dimensional Model of a Discharge
Channel Using Digital Images.
C.2 Paper Description
The paper describes the ground work for the system, which details the development
of a system that converts 2D images of a discharge channel into a 3D model. The
discharge was created in a controlled environment using impulse generator. Digital
capture devices were placed in five different configurations to investigate optimal
placement. A 550 kV impulse discharge with arc length 0.83 m was captured using
three wireless web-interface cameras. Optical and digital filtering was used to pre-
processing of the images before the 3D modelling stage. A software application
was developed for the model reconstruction, which was implemented in the form
of an adaptable modelling framework. A simple modelling algorithm has been
implemented to complete the proof of concept. The model ultimately can be used to
aid in understanding the shape, formation and propagation of a lightning discharge
channel for scientific research.
LABORATORY INVESTIGATION INTO RECONSTRUCTING A 
THREE DIMENSIONAL MODEL OF A DISCHARGE CHANNEL 
USING DIGITAL IMAGES 
Y. C. Liu, A. J. Rapson and K. J. Nixon 
University of the Witwatersrand, School of Electrical and Information Engineering, Johannesburg, South Africa 
Abstract. This paper details the development of a system that converts two dimensional (2D) images of a discharge 
channel into a three dimensional (3D) model. The discharge was created in a controlled environment using impulse 
generator. Digital capture devices were placed in five different configurations to investigate optimal placement. A 
550 kV impulse discharge with arc length 0.83 m was captured using three wireless web-interface cameras. Optical 
and digital filtering was used to pre-processing of the images before the 3D modelling stage. A software application 
was developed for the model reconstruction, which was implemented in the form of an adaptable modelling 
framework. A simple modelling algorithm has been implemented to complete the proof of concept. The model 
ultimately can be used to aid in understanding the shape, formation and propagation of a lightning discharge channel 
for scientific research. 
 
Key words. 3D Modelling, Computation, Framework, Image Filtering, Lightning Photography, SPARKY. 
 
1. INTRODUCTION 
The advancement of technology in the field of 
computer processing power and rendering 
capabilities has provided the platform to create three 
dimensional (3D) models of discharge channels. 
Such models can be used to determine many aspects 
of a discharge channel, namely the arc length, the 
angles at the origin, termination, branches, and speed. 
Ultimately, the objective would be to reconstruct a 
discharge channel on a large scale, such as High 
Voltage (HV) arcs in the form of lightning, and 
equipment flashovers.  
A software application was developed to reconstruct 
a 3D model of a discharge channel from digital 
images. This is a preliminary investigation into the 
reconstruction of a 3D model, which will ultimately 
provide a proof of concept. The application was 
tested by creating a discharge channel within a 
controlled environment. An impulse discharge, 
replicating a lightning discharge was elected for 
testing, as it is the more challenging discharge to 
capture digitally. If the test for an impulse discharge 
is proven successful, all other discharge types would 
be easier to implement. This experiment is a small 
scale contribution toward a practical application. The 
final aim for the system is to provide a solution that 
is cost effective, abstracts the user from complexity 
and has an adaptable modelling system. 
An investigation on previous work in this field is 
presented. Using new techniques and the results from 
previous work it was possible to develop a suitable 
methodology. In this paper the modelling framework 
is briefly discussed, the experimental setup is 
explained and execution is examined. The testing 
procedure and obtained results will be presented, 
followed by a discussion of suitable applications and 
future work requirements. 
2. BACKGROUND 
A brief discussion on existing solutions pertaining to 
aspects of the problem is produced. This includes an 
examination of past solutions and the problems 
relating to the photography of an impulsive 
discharge. 
2.1 Previous Solutions 
Creating a 3D model of a discharge channel is not a 
new concept. In 2005 John Morkel and Brian Wylie 
used still analogue cameras and advanced neural 
networks to capture and generate a model [1, 2]. 
While their work demonstrates that modelling of a 
discharge channel is possible, much work needs to be 
done before a completed modelling solution is 
developed. 
2.2 Photography of an Impulse Discharge 
The duration of a typical pulse of a lightning 
(otherwise referred to as an impulse) discharge only 
lasts approximately 30-90 µs [3]. To capture a 
channel of such a short interval onto an image, 
suitable capture devices need to be acquired. Data 
acquisition techniques differ between the 
implementation of digital and analogue photography 
methods. The exposure time must be reduced such 
that the intense light produced by the discharge does 
not overexpose the image sensor (digital) or the film 
(analogue). The relevant information desired for 
capture is specifically the visual wavelengths of light. 
3. APPROACH/METHODOLOGY 
The approach developed to generate, capture and 
model a discharge channel is divided into two 
sections, namely the modelling framework and the 
experimental setup. The modelling framework covers 
the software and imaging techniques to create the 
model. The experimental setup involves the 
generation and capture of the impulse discharge 
channel. A broad overview of the approach is 
illustrated in Figure 1. 
 Figure 1: Overview of the approach developed. 
4. MODELLING FRAMEWORK 
The adaptive modelling framework developed is 
named SPARKY, as it models HV discharges in 3D 
space. The framework is open source (under the 
GNU General Public License, version 3), to allow 
future developers to easily expand and adapt the 
framework to their needs and enhance the initial 
functionality. SPARKY is cross-platform, 
independent of the underlying operating system, 
allowing it to be run on almost any platform. This 
ensures that the framework can be adapted to any 
configuration.  
4.1 SPARKY Architecture 
In order to provide an interactive model, a suitable 
rendering library is required. To reduce the time 
required for development, a pre-existing library is 
used. The library chosen for this framework is 
Visualization Toolkit (VTK), as it is free for use and 
has been extensive testing [4]. 
The architecture of SPARKY is established over 
several layers. Each layer interacts with the layer 
above and below, as illustrated in Figure 2. This level 
of abstraction helps to decouple the layers from the 
implementation of classes that surround it. The 
interaction between the various layers use well 
defined interfaces, to ensure proper operation. 
Operating System
User Interface
SPARKY Core
Visualization Toolkit (VTK)
Graphics
Interfaces
 
Figure 2: Architecture illustrating layer interaction. 
The User Interface provides both a command line 
interface for user input and an interactive rendering 
window. The information is exchanged between the 
User Interface and the underlying framework via 
SPARKY Core. In order to save and load digital 
images and models, a set of readers and writers are 
grouped under InputOutput. As VTK is not part of 
the code implemented in SPARKY, Interfaces are 
required. To ensure that the digital images meet the 
requirements for the modelling, Filtering is required. 
The modelling algorithms are stored under 
Modelling. Rendering provides abstraction between 
SPARKY and VTK for the interactive model. To aid 
in debugging a simple Logging system is provided. 
4.2 Digital Filtering 
The use of digital filters is necessary to process the 
images to usable data. SPARKY requires monotone 
images of identical sizes. 
 
(a) 
 
(b) 
 
 
 
 
(c) 
Figure 3: An image processed using various digital 
filters (a) smoothing filter, (b) black and white 
Boolean filter (c) track, compare and crop. 
The images in Figure 3 display a progression of the 
three filter layers used in the digital filtering process. 
A smoothing filter in Figure 3 (a) levels out the edges 
of the discharge. The black and white Boolean filter 
in Figure 3 (b) converts the greyscale image to a 
monotone image, representing the discharge as pure 
white pixels and redundant information as pure 
black. The filter in Figure 3 (c) tracks the discharge 
within the frame and extrapolates the discharge 
information and cropping the significant data from 
the image. A set of images are processed through the 
last filter to obtain the maximum size of the 
discharge. This filter takes into consideration the 
rotation required of the individual image. The images 
are resized to the maximum dimensions of the 
discharge, and cropped so that the image sizes are all 
identical. 
4.3 Three Dimensional Placement 
Figure 4: Basic model reconstruction method. 
In order to reconstruct the model, the digital images 
need to be placed to match the experimental setup, as 
illustrated in Figure 4. Placing the images in 3D 
space before being modelled, allows for the 
algorithm to focus on determining a model without 
any image processing requirements.  
The captured images can be rotated to correct for 
camera orientation, such as clockwise, counter-
clockwise and a full 180˚ as necessary. 
4.4 Generating the 3D Model 
As the algorithm is non-trivial, it has been divided 
into several modules, each performing a single task. 
The current implementation is able to use two or 
three images to generate a model. The interaction 
between the three core modules is presented in 
Figure 5. The division of the algorithm supports 
abstraction during the implementation. 
 
Figure 5: Core modules for the reconstruction 
algorithm. 
The algorithm is simplified to layers along the y-axis. 
This method eliminates the third dimension, reducing 
the algorithm to a 2D problem. Normals of the white 
segments (discharge) are projected to the origin of 
the setup, where they are compared to the normals 
from other perspectives (as shown in Figure 4). The 
normals for all the images are generated in the 
Generate Normals module. This module ensures that 
only a full valid set of normals is generated. The 
normals are used in Reconstruct the 3D Model to find 
the points of intersection. These points are used to 
generate the cylinders that define the model. 
If the end-user enables the option to average the 
cylinders, the module Average the Model is called. 
This module determines a single cylinder for every y-
axis (height). This option cannot be used when 
modelling branched discharge channels. 
A second option (only available for three image 
reconstructions), First Detect, can be invoked by the 
user. This option adjusts the algorithm to define the 
first circle as valid, and the remaining ones as 
possible. These remaining circles are then only valid 
if additional images can verify them. 
4.5 Rendering 
The rendering process in SPARKY is a two step 
process: capture the 3D model back to 2D images for 
analysis, and provide an interactive model. The 
model is automatically captured by placing the 
camera as in the experimental setup and saving a 
screenshot, which is repeated for all angles. After this 
is completed, the end user can interact with the 
model by altering the camera by: panning, zooming, 
rolling, varying the azimuth, and elevation. 
5. EXPERIMENTAL SETUP 
The experimental setup examines the setup 
concerning the HV laboratory; the equipment 
required for digital capture and camera placement 
considerations. 
5.1 High Voltage Laboratory 
The HV laboratory provides a means to produce an 
impulsive discharge channel within a controlled 
environment. This provides a predetermined position 
of a discharge for experimentation and offers a 
predictable voltage level of the discharge. The 
experiment in the HV laboratory replicates a 
downward positive lightning discharge. The general 
setup of the HV laboratory is illustrated in Figure 6. 
Figure 6: Experimental setup for data capture of a 
discharge channel. 
An impulse (Marx) generator was used to create the 
highest direct current (dc) voltage as possible [5]. A 
gap length of 0.83 m was produced, which 
determines the height of the discharge channel. The 
breakdown in air was obtained at approximately 
550 kV with the given gap length. The gap setup 
used a rod-to-rod configuration, which primarily 
provided a single branchless channel.  
5.2 Digital Capture 
There are two stages to the photography of the 
discharge: the capture device considerations 
(acquisition and configuration), and optical filtering. 
The device selected for digital capture was the Axis 
207W wireless web camera [6], primarily used for 
surveillance purposes. The image sensor available in 
this camera is a CMOS sensor. The camera has a 
maximum frame rate of 30 frames per second (fps) 
and a resolution of 640 × 480. Three of these cameras 
were used to investigate three different angular 
perspectives of a discharge for 3D reconstruction. 
This camera was chosen for a number of reasons: 
networking capabilities; wireless option; web 
interface; triggering options; cross platform operating 
system potential; additional functionality and output 
formats. Disadvantages of using these cameras were 
the limited image quality, fixed iris, no zooming 
functionality and a high start up current. The cameras 
are protected from interference caused by the 
discharge by floating the circuit on an isolation 
transformer. 
(a) (b) (c) 
Figure 7: Images captured with various optical filters 
(a) cross polarised filter, (b) cross polarised and 
infrared filter, and (c) cross polarised, infrared and 
violet filter. 
One of the challenges of capturing image data on a 
discharge channel is the high light intensity 
associated with it. Optical filters were used to isolate 
relevant information in the frame. The images in 
Figure 7 display a progression of three filter layers 
used to isolate the visible wavelengths of light. The 
first filter in Figure 7 (a) consists of a cross polarised 
filter, which dampens the amount of visible light 
reaching the capture device. The second filter in 
Figure 7 (b) was added to reduce the amount of 
infrared, and the third in Figure 7 (c) reduced violet 
wavelengths. 
 (a) (b) (c) 
Figure 8: Captured images at 90° angle separation 
(a) on camera 1, (b) on camera 2, (c) on camera 3. 
Error! Reference source not found. displays a 
typical set of optically filtered images resulting from 
this stage. The cameras were synchronised using a 
network time protocol server. A pre-trigger time 
buffer was set to ensure that the relevant information 
is captured. The camera was activated by a website 
trigger. The information was managed using a file 
transfer protocol server. The information was 
received as individual JPEG files. The discharge only 
appeared on one of the incoming frames, which was 
expected due to the low frame rate.  
5.3 Camera Placement 
Optimal placement of the devices was required for 
reconstructing the 3D model of the discharge. There 
were several factors that needed to be taken into 
account: location, height, distance, and angles. The 
location was important to consider for safety reasons. 
The capture devices needed to be protected against 
the HV discharge, whereby a safety perimeter was set 
up at a radius of 1.7 m away from the intended 
discharge. Identical heights were accomplished at 
1.035 m above the ground. The distances of each 
capture device to the intended striking area were 
determined by the specific focal length of the device, 
such that the captured image contained the same 
height of the discharge arc. The capture devices were 
placed in several angular formations to establish 
optimum camera angles. The formations also 
provided feedback on the accuracy of the 3D 
algorithm. There were five angles tested: 30°, 45°, 
60°, 90°, and 120°. This provided a wide range of 
angles to evaluate results. 
6. TESTING PROCEDURE 
The testing of the entire system provides a means of 
determining the accuracy of the model, while 
ensuring that the software operates without error.  
6.1 Software 
To ensure that the source code developed for the 
framework performs as expected, several testing 
techniques were used. These techniques include: 
validation of the user requirements, proving the 
source code is functional, obtaining results from end-
user tests and verification of platform independence. 
There are four definitions that can be used to measure 
the overall effectiveness of the design as a 
framework. 
Maintainability: As the framework was developed 
using a prototyping approach, the source code 
implemented is not highly maintainable, requiring 
preventive maintenance to be performed. No 
perfective maintenance is required as the end-user 
requirements have been achieved. 
Functionality: Functionality is defined as the ability 
of the software solution to meet requirements when it 
is used under specified conditions [7]. When 
considering the overall requirements, it can be seen 
that the overall system is functional. 
Reliability: Reliability refers to the ability of the 
software solution to maintain a level of performance 
under specified conditions [7].  With the limited 
sample data sets, the overall system performs 
consistently with no visible problems. The 
framework appears to be reliable. 
Coupling: Coupling is used to measure how 
dependant classes are on one another [7]. From the 
architecture, it is clear that the underlying VTK 
library interfaces directly with seven of the units, 
making the framework extremely coupled to VTK. 
6.2 Algorithm 
The testing procedure for the algorithm was used to 
determine if the models could be used for scientific 
research. The testing was performed using two 
independent tests:  
a) A visual comparison of the input images to the 
model, dependent on human judgement is made.  
b) A tester application, SPARKY Tester, was 
developed to detect inconsistent pixels in the 
images and return a percentage error. 
The visual comparison indicated the overall tracking 
of the model to the discharge, while the tester 
application provided a percentage error.  
Table 1: Testing procedure used for model analysis. 
Case Images Required Average First Detect 
001 3 Yes Yes 
002 3 Yes No 
003 3 No Yes 
004 3 No No 
005 2 - Yes 
006 2 - Yes 
007 2 - Yes 
 
The model can be rendered by altering the algorithm 
configuration, as discussed in Section 4.4. Table 1 
displays the seven different test cases implemented 
for each set of images. A total of seventy tests were 
presented for all the cases and angles. 
7. RESULTS 
Screen shots were taken of the 3D models in the 
angular placements of the original images. Two types 
of testing were implemented: visual assessment and 
pixel comparison techniques. Since a discharge 
channel cannot be reproduced, it was difficult to 
verify which angle produced the optimum solution. 
Only two sets of images were taken from each 
angular configuration, due to limited experimental 
time. The results from the pixel comparison tests are 
displayed in Table 2.  
Table 2: Results from all the test cases in each 
camera angle configuration. 
 
Case 
Percentage of pixel mismatch (%) 
30° 45° 60° 90° 120° 
001 10.59 8.43 8.01 11.84 12.51 
002 9.07 13.20 13.02 13.27 11.95 
003 18.47 6.94 15.12 10.70 9.83 
004 10.29 13.55 12.43 12.56 11.30 
005 8.06 6.35 9.70 11.96 12.30 
006 12.96 14.09 10.87 10.29 12.32 
007 9.23 10.33 7.77 - 6.92 
Average 11.24 10.41 10.99 11.77 11.02 
 
It was observed that camera placements at 45° 
provided the least percentage error of 6.35 %. This is 
an acute angled configuration that can only provide 
images for a limited perspective of the discharge. It 
was not possible to validate the perspectives on the 
opposite region of the channel. The quantised results 
from SPARKY Tester in Table 2 present an overall 
error of approximately 11%. 
8. DISCUSSION 
There are several areas which can be improved upon 
to provide a complete solution. The expansions 
expected for the modelling framework and camera 
placement are presented. 
8.1 Modelling Framework 
As the framework is still under development, there 
are several factors that currently limit the framework: 
c) User Interface: Define an adaptable graphical 
user interface to transfer information. 
d) Improve the Filtering and Modelling hierarchy: 
Allow for better integration of future modules. 
e) Due to interfacing issues to the VTK library, 
smart pointers have not been implemented 
throughout all the classes. 
f) The underlying code is not decoupled 
sufficiently from VTK and wrapper classes need 
to be implemented. 
These four limitations need to be resolved before 
further functionality is added, to reduce underlying 
framework errors.  
8.2 Camera Placement 
Accurate comparison of the angular configurations 
can only be achieved with an array of multiple 
cameras arranged in the required formation. This will 
provide an adequate number of images for 
comparisons over a single discharge. This needs to be 
supplemented with a precise camera placing strategy. 
If the cameras can be placed more accurately, 
comparisons with reconstructed model results could 
be more adequately achieved.  
8.3 Future Work 
There are two main reasons for developing this 
product. Firstly, it allows more scientific research 
based on natural lightning by mounting cameras 
around high-rise buildings. Secondly, this principle 
can be expanded to use x-ray plates to capture the 
propagation of the strike through the earth’s surface. 
Before this solution can be implemented for 
applications in scientific research, several areas of 
expansion are required.  
8.4 Modelling Framework 
The framework functionality can be expanded as 
follows: 
Video Playback: To enable end-users to view the 
propagation of the lightning strike, the framework 
must be expanded to allow multiple images to be 
loaded. These images must then be modelled 
individually and provide an interface similar to a 
video recorder, to step through the sequence of 
models. 
Modelling Libraries: The advanced modelling 
algorithms require external libraries for 
implementation. Based on the algorithm, suitable 
libraries must be sourced and tested. The models can 
then be tested to determine their suitability for 
scientific study. 
8.5 Digital Capture 
The solution can be improved by implementing 
capture devices with additional functions, such as 
optical zoom, iris exposure control. Zoom functions 
would improve the image size and quality, also 
provide extra safety for the devices. The function for 
iris control would improve the exposure of the image, 
allowing for a more accurate capture of the 
discharge.  
An extension to the project would include a fourth 
dimension: time. The frame rate required for this 
option is expected to be in the range of 100,000 fps. 
This would ultimately provide a 3D reconstruction of 
a lightning discharge channel propagating through 
space. 
8.6 Testing Procedure 
The analysis of the system results requires a high 
level of user interaction. A more automated system 
needs to be developed. The system should return the 
error to the user with the rendered model. This will 
enable the user to interpret the model without 
additional steps. 
9. CONCLUSION 
The overall solution was implemented to prove the 
plausibility of the concept. As a result, the system 
was successfully executed to produce 3D 
reconstructed models of lightning discharges from 
several a single framed images. The modelling 
framework was analysed to indicate future work that 
needs to be performed, before the addition of more 
advanced algorithms should be considered. 
The algorithm that was designed can create a model 
from two or three images. When using three images 
for reconstruction, the model error increases, due to 
misalignment of the individual cameras placement 
and limitations on the implemented algorithm. The 
quantised modelling error provides a total inaccuracy 
of only 11%; on top of that several improvements can 
be added as extensions to the already acceptable 
solution. The inaccuracy of the model shows that it is 
not suitable for scientific research. 
The impulse discharge was successfully captured 
using the Axis 207W capture devices and 
extrapolated using a combination of optical and 
digital filters. An optimal angular placement was 
obtained at 45° camera separation. The captured data 
was usable for reconstructing the visible light emitted 
from a discharge.  
The implementation of the future work indicated in 
this paper will further expand this solution from a 
plausible concept to a practical application.  
ACKNOWLEDGEMENT 
The authors would like to thank Eskom TESP, 
THRIP and the NRF for funding this research. They 
also express their gratitude to CBi-electric: low 
voltage for funding of the Lightning/EMC Research 
Group and for support of the CBi-electric Chair of 
Lightning. 
REFERENCES 
[1] J. Morkel, “3D Reconstruction of Electrical Discharge 
Channels From 2D Images: Image Processing and 
Reconstruction Algorithm”, School of Electrical and 
Information Engineering, University of the Witwatersrand, 
South Africa, 2005. 
[2] B. Wylie, “3D Reconstruction of Electrical Discharge 
Channels from 2D Images: Simulated Lightning Model and 
Photography of Laboratory Discharges”, School of Electrical 
and Information Engineering, University of the 
Witwatersrand, South Africa, 2005. 
[3] V. A. Rakov, M. A. Uman, Lightning – Physics and Effects, 
Department of Electrical and Computer Engineering, 
University of Florida, Cambridge University Press, 2003. 
[4] Kitware, The Visualisation Toolkit User’s Guide, Kitware 
Inc., www.kitware.com, Version 5, 2006. 
[5] E. Kuffel, W.S. Zaengl, J. Kuffel, “High Voltage 
Engineering”, Pergamon Press, 1984. 
[6] Axis Communications AB, “AXIS207 User’s Manual Rev 
3.0”, August 2006. 
[7] H. van Vliet, Software Engineering, Principles and Practice, 
John Wiley and Sons Ltd, New York, Second edition, 2002 
124
Appendix D
High Voltage Testing on Large
Channel Paths with Discontinuities
D.1 Preamble
This appendix is a paper that was accepted and presented for publication by the
International Symposium on High Voltage Conference (ISH) in 2011, hosted in
Hannover, Germany. The paper is entitled: A Method of Creating Graphical
3D Reconstructions of High Voltage Discharge Channels Using Digital
Images.
D.2 Paper Description
The paper briefly describes the three-dimensional reconstruction system and tests
the capability of the system with an irregular gap geometry in the SABS high voltage
testing laboratory at NETFA. Two image perspectives of each flashover were taken
from a 5.85 m floating object setup of switching impulse U50 tests. This investigation
marks the first usage of Axis P1344 cameras. An example of the reconstruction
process is provided of the discontinuous irregular discharge channel shape and
presents the reconstruction in the three-dimensional interactive environment. The
paper concludes the successful reconstruction of single-channelled flashover discharge
channels with with a discontinity.
A METHOD OF CREATING GRAPHICAL THREE-DIMENSIONAL RECONSTRUCTIONS 
OF HIGH VOLTAGE DISCHARGE CHANNELS USING DIGITAL IMAGES 
 
Y.C.J. Liu1*, K.J. Nixon1, I.R. Jandrell1  
1
 School of Electrical and Information Engineering, University of the Witwatersrand,  
Johannesburg, South Africa, 
*Email: Yu-Chieh.Liu@wits.ac.za 
 
Abstract: This paper describes a method used for graphically reconstructing three-
dimensional flashover discharge channels within an interactive virtual environment. The 
system for reconstructing high voltage discharge channels is presented, with an example 
of the reconstruction process using tests from a 5.85 m floating object setup of switching 
impulse U50 tests. This work provides the possibility of studying photographed flashover 
events in the form of a reconstructed model with the ability to zoom, tilt and rotate the 
channel within a three-dimensional environment. 
 
 
1 INTRODUCTION 
Flashover is often a desired effect in high voltage 
testing, but in the case of flashover occurring in 
live, operating equipment, the resulting damage 
can be catastrophic. Burn marks, damaged 
insulation and carbon by-products are usually the 
only visual indication of failure due to flashover. 
Even if an operator is available to witness the 
failure, the naked eye may not be able to fully 
perceive the extent of damage, as the discharge 
channel of a flashover is fast and almost 
instantaneous with µs durations. 
By obtaining a three-dimensional (3D) 
representation of a flashover discharge channel, 
the channel can be properly analysed in a three-
dimensional visualised space. This paper will 
discuss the three-dimensional reconstruction of 
single-channelled flashover discharges from a 
large floating object setup, a total gap length (from 
high voltage electrode to earth electrode) of 
5.85 m. An example will be presented throughout 
this paper, from the image acquisition to the 
completed reconstructed model. 
2 BACKGROUND 
Although it is not customary to photograph high 
voltage discharge channels in the laboratory, 
similar discharge channels are usually 
photographed in the form of lightning. With the 
development of more sophisticated camera 
technology, a move toward high speed cameras 
has opened up even more possibilities in 
researching the mechanisms behind these fast-
occurring transients. In addition, there are obvious 
visual parallels that can be drawn between 
lightning and high voltage flashover channels. This 
paper makes use of only standard speed camera 
images of flashover channels to demonstrate a 
reconstruction procedure that can be extendable to 
high speed camera footage. 
There is significant value in understanding the 
physical distribution of a high voltage discharge 
channel, as this is often an indication of 
weaknesses in equipment designs and 
understanding how the electric fields are affected 
in live-testing. The physical distribution of high 
voltage discharge channels is typically considered 
using photography of the discharge channel from a 
single perspective.  
One photographic perspective also lacks the ability 
to fully grasp the spatial propagation of the 
channel, which highlights a need to develop a 
system that is capable of reconstructing a 
discharge channel within three-dimensional space. 
3 SYSTEM OVERVIEW 
A system was designed and developed to 
reconstruct high voltage discharges in three 
dimensions using photographic images coupled 
with the locations of cameras in relation to the test 
setup. An important feature of its design is the 
reusability of the system to different types of 
discharge channels, which specifically takes 
Boolean black and white images discharges as 
inputs. This system was previously tested using 
0.83 m long single-channelled high voltage 
discharges in a small scale test [1], [2], and in a 
lightning environment using one image of a 
branched lightning discharge as a preliminary 
investigation [3]. Each of these tests proved to be 
successful in reconstructing a three-dimensional 
model from test images. 
Figure 1 provides a block diagram representing 
each stage of the reconstruction process. This 
paper describes an overview of the modelling 
procedure; from obtaining photographs of the high 
voltage discharge channels, to creating the models 
in a three-dimensional interactive virtual 
environment. 
 Figure 1: Overview of the system for the three-dimensional lightning reconstruction application.
3.1 Reconstruction Application 
The reconstruction framework and algorithm was 
developed in C++ using a visualization toolkit 
library (VTK). The application framework accepts 
two or three image perspectives as inputs to the 
system. Two image inputs enable the 
reconstruction of single-channeled discharges, and 
three image inputs enable reconstruction of 
multiple channeled discharges. 
 
3.1.1 Image Processing   An image of a flashover 
often includes extra information that is not required 
in the reconstruction of the channel. The 
framework includes a number of built-in automated 
digital filters to eliminate this redundant 
information. These filters replace pixels that 
represent the discharge channel with white pixels 
(pixel value of 255), and negative space 
information as black pixels (pixel value of -255). 
Depending on the quality of the input images, 
manual image processing may be implemented to 
correctly categorise ambiguous grey pixels. 
3.1.2 Reconstruction Algorithm   The digitally 
processed images are placed in the three-
dimensional virtual environment in corresponding 
position to original relative camera positions as 
demonstrated by Figure 2a for 90º camera 
separations. In this example, the simplest 
demonstrative sets of data are used; i.e. mirror 
images of the branched data, and a flat 90º angle. 
The reconstructed flashover discharge channel is 
centred about the y-axis (i.e. x = 0 and z = 0) in 
this virtual environment. 
The modelling problem is three-dimensional and 
can be complicated if all the dimensions are 
tackled at once. Therefore, the modelling algorithm 
has been simplified to a series of two-dimensional 
geometric problems. For example, consider a 
single-channelled discharge channel that has two 
camera perspectives demonstrated in Figure 2b. 
Looking at the scenario from a bird’s eye view, the 
first white pixel band at the top of each image 
extends three perpendicular normals from each 
image towards the y-axis. Each normal is extended 
from a specific point in the one-pixel high band of 
white pixels. The points are demonstrated in Figure 
2b and listed below: 
a. Leftmost white pixel 
b. Rightmost white pixel in a continuous band 
c. Middle position between point a. and b. 
The middle normals of each image are compared 
for an intersection. If an intersection between the 
normals exists, a one-pixel high cylinder is created, 
The intersection points of the leftmost and 
rightmost white pixel positions are used to 
calculate the radius of the cylinder as 
demonstrated in Figure 2b. This process is 
repeated to produce a reconstructed model that is 
constructed by a series of stacked cylinders.  
This method fails if the channel width is too thin 
(i.e. one or two pixels wide), and when the angle of 
separation between the perspectives is too small, 
i.e. less than 30º or too oblique (150º-210º). 
y
xz
 
(a) 
 
(b) 
Figure 2: A graphical representation of the three-dimensional reconstruction algorithm which reduces the 
problem to a series of two-dimensional geometric solutions. (a) Processed lightning images placed in at 
positions of 90º-separations in a three-dimensional virtual environment with a simple representation of 
extended normals to reconstruct a channel. (b) Overhead two-dimensional perspective with relevant points in 
a data image extending geometric normals towards the y-axis. 
  
(a) (b) 
Figure 3: Physical laboratory setup (a) Floating object U50 setup with varying gap distances dG1 and dG2. 
(b) Two camera setup, laterally separated by 94º in relation to the DUT (experimental setup).  
 
Table 1: Gap configurations recorded during U50 
tests of the floating object setup in Figure 3a. 
Gap 
Configuration 
dG1 (mm) dG2 (mm) 
1 1170 3510 
2 1560 3120 
3 1950 2730 
 
4 EXPERIMENTAL SETUP 
The experimental setup will discuss specifics of the 
gap configuration and the camera setup. 
4.1 Discharge Environment 
Image test datasets of flashovers were obtained 
from a floating object, double rod-to-rod gap 
configuration in air, with rounded tip electrodes. 
The gap configuration is illustrated by Figure 3a, 
where dG1 is the distance of the gap between the 
high voltage electrode and the floating object and 
dG2 is the distance of the gap between the lower 
portion of the floating object and the ground 
electrode. 
A U50 test procedure was implemented to the setup 
using a 90/3010 µs switching impulse with an 
approximate peak voltage of 1.45 MV applied to 
the high voltage electrode at the top of the setup. 
Iterations of the gap configuration were obtained 
by varying the position of the floating electrode 
between the fixed high voltage and earth 
electrodes. Of the full range of U50 tests, three gap 
configurations were recorded, which are presented 
in Table 1.  
4.2 Image Acquisition 
Two camera perspectives were used during the 
U50 tests of the floating object setup. Figure 4a and 
4b show the two perspectives of the same 
flashover of one gap configuration 1 breakdown 
(taken from Table 1). The cameras were placed 
approximately 13 m away from the test setup 
(DUT) with a lateral separation of 94º. Figure 3b) 
indicates the general floor plan with the camera 
positions in relation to the experimental setup. 
Identical surveillance cameras were used, which 
have several specific functions that allowed for 
automating the recording process, listed below: 
1. 8-20 V input power 
2. Trigger by motion detection 
3. Pre-buffer 
4. Local memory storage 
Given the large input voltage range of the 
cameras, each camera was electrically isolated 
during the test runs, using small 12 V (5 Ah) lead 
acid batteries. The customisable motion detection 
functionality enabled the camera to trigger without 
any manual intervention. A one second pre-buffer 
was implemented to ensure information was not 
lost, and 3-second duration videos were stored on 
a local removable SD card. 
The cameras were operating at 15 frames per 
second with image dimensions of 1280 × 800. 
These settings produced videos with one or two (or 
none) frames with flashover image information. 
  
 (a) Camera 1 (0º) 
 
 
 
(b) Camera 2 (94º) 
Figure 4: Sample set of images of flashover occurring over a floating object with Gap Configuration 1 as 
presented in Table 1 for three-dimensional reconstruction. 
 
(a) 
 
(b)  (c) 
 
 (a) 
 
(b) 
 
(c) 
(i) Perspective 1 (0º) 
 
(ii) Perspective 2 (94º) 
Figure 5: Reconstruction model input images and correlating images of outputs. (i) Perspective 1 relating to 
Camera 1 at an angular reference of 0º. (ii) Perspective 2 relating to Camera 2 at 94º of Camera 1. 
(a) Digitally filtered image. (b) Three-dimensional reconstruction in three-dimensional environment. (c) Test 
image presenting the difference between image (a) and (b). 
 
Figure 6: Three-dimensional model in the virtual interactive environment, flanked by image data on either 
side. Perspective 1 image place at 0º (right) Three-dimensional reconstruction  (middle) Perspective 2 image 
place at 94º (left). 
5 MODEL AND VIRTUAL ENVIRONMENT 
The channel information is isolated from the 
original images through digital filtering, in Figure 5a 
– for perspective 1 and 2 (i and ii). The digital 
filtering process also required a manual scaling of 
images, to ensure that the correct comparative 
data is used. The three-dimensional model is 
constructed using the digitally filtered images and 
the resulting an image of three-dimensional model 
taken at the same corresponding angle to the 
original perspective for comparison, as 
demonstrated in Figure 5b. 
Figure 6 illustrates a sample window of the 
interactive virtual environment, featuring the 
reconstructed flashover model demonstrated in 
Figure 5. The reconstructed model is placed in the 
centre of the setup, with a set of x-y-z axes at the 
base of the model. On either side of the model is 
the digitally filtered images (placed in respective 
positions to the original perspectives), of which 
normals were extended from in order to create the 
model.  
6 TESTING 
Visually, it is evident that the reconstructed model 
correctly follows the path of the flashover channel 
in the image. As the original flashover channel 
information can only be projected from the 
photographed information, the testing procedure 
primarily tests the accuracy of the reconstruction 
algorithm, by comparing input data to output data. 
Figure 5c – for perspective 1 and 2 (i and ii) – 
demonstrates an image highlighting (with white 
pixels) the difference between the digitally filtered 
image and the image of the model in the 
corresponding perspective. 
It can be seen that perspective 2 demonstrates a 
larger mismatch in pixels, than perspective 1. This 
is expected, since part of the original image is 
over-exposed due to the recording mechanics of 
CMOS camera chips. Since the reconstruction 
algorithm takes the average width of the channel 
from each of the images, it could be assumed that 
the reconstructed model is represented as thicker 
than it should be. This is also buffered by the fact 
that the photographed channel width is dependent 
on the exposure time of the CMOS sensors, which 
would vary for individual cameras operating on 
isolated circuits. 
7 FUTURE WORK 
The reconstruction of single-channelled flashover 
discharges does not demonstrate the full capability 
of the reconstruction system. Tests using simple 
discharge channels will be implemented in the 
future, which would include complex lightning 
channel structures. 
Currently, there is a significant amount of manual 
modifications that are made in the digital filtering 
process, which is mostly represented by the 
manual scaling of images. Future work requires the 
implementation of an automated reconstruction 
system. 
Furthermore, since current methods of testing only 
consider image mismatches, a more accurate and 
comprehensive testing framework needs to be 
implemented to quantify the error associated with 
the reconstruction algorithm – this will have a large 
effect on branched channel structures. 
8 CONCLUSION 
The algorithm has been shown to provide 
successful path reconstructions of single-
channelled flashover discharge channels, for a 
floating object experimental setup. Further 
investigations include the three-dimensional 
reconstruction of branched channels and complex 
lightning channels. Several modifications need to 
be implemented to the current system for better 
automation and an accurate testing framework. 
9 ACKNOWLEDGMENTS 
The authors would like to thank Eskom for the 
support of the High Voltage Engineering Research 
Group through the TESP programme. They would 
also like to thank CBI-electric for support, the 
department of Trade and Industry (DTI) for THRIP 
funding as well as to the National Research 
Foundation (NRF) for direct funding. 
 
10 REFERENCES 
[1] Liu, Y.C. Rapson, A.J. Nixon K.J, “Laboratory 
Investigation into Reconstructing a Three-
dimensional Model of a Discharge Channel 
using Digital Images”, SAUPEC – 
Stellenbosch, South Africa, Vol. 18 pp. 83, 
2009. 
[2] Liu, Y.C. Nixon, K.J. Jandrell, I.R., “Preliminary 
Investigation into Three-Dimensional 
Reconstruction of Laboratory High Voltage 
Discharges using Photographs taken from 
Different Elevation Perspectives”, Ground LPE 
– Salvador, Brazil, Vol. 4, No. P8, 2010. 
[3] Liu, Y.C. Nixon, K.J., “A Preliminary 
Investigation into 2D Reconstruction of 
Branched Lightning Discharge Channels in a 
3D Environment”, SAUPEC – Johannesburg, 
South Africa, Vol. 19 No. G-2 pp. 295-299, 
2010
 
130
Appendix E
Small-Scale Investigation on
Reconstruction with Cameras at
Different Elevations
E.1 Preamble
This appendix is a paper that was accepted and presented for publication by the In-
ternational Conference on Grounding and Earthing & 4th International Conference
on Lightning Physics and Effects Conference (LPE) in November 2010, hosted in
Salvador, Brazil. The paper is entitled: Preliminary Investigation into Three-
Dimensional Reconstruction of Laboratory High Voltage Discharges us-
ing Photographs Taken from Different Elevation Perspectives.
E.2 Paper Description
This paper describes the investigation on processing discharge channel reconstruc-
tions with cameras at different elevations at relatively small angular variations.
Limited conclusions can be made on this investigation, but it can be shown that
reconstructed model qualities are dependent on the image qualities from the cameras.
 GROUND’2010 
 
& 
 
4th LPE 
 
 
International Conference on Grounding and Earthing 
& 
4th International Conference on                                     
Lightning Physics and Effects  
 
Salvador - Brazil          November, 2010 
 
 
PRELIMINARY INVESTIVATION INTO THREE-DIMENSIONAL RECONSTRUCTION OF LABORATORY HIGH  
VOLTAGE DISCHARGES USING PHOTOGRAPHS TAKEN FROM DIFFERENT ELEVATION PERSPECTIVES 
 
Yu-Chieh J. Liu      Ken J. Nixon      Ian R. Jandrell 
School of Electrical & Information Engineering, University of the Witwatersrand, Johannesburg, South Africa 
 
 
Abstract – High voltage discharge channels have been re-
constructed in three-dimensions using photographic im-
ages at different height perspectives. This work precedes 
the reconstruction of lightning discharges attaching to tall 
towers, in particular, Brixton Tower in South Africa. One of 
the challenges presented in this environment includes the 
selection of camera locations facing the tower which will 
likely be associated with height perspectives. The results of 
preliminary small scale tests performed in the high voltage 
laboratory are presented for a 0.66 m gap with elevation 
angles between 0º-18º. It is found that the two cameras pro-
vide inconsistent image data, which may require a pre-
processing stage for three-dimensional reconstruction. 
 
1 - INTRODUCTION 
 
The study of lightning activity at tall structures has been 
an integral part of research into the meteorological phe-
nomenon. At present, most lightning research using opti-
cal recordings has mostly been limited to two-
dimensional perspectives. Several papers detail the use 
of two camera perspectives used to provide depth per-
ception of the channel [1-3], but none have attempted a 
three-dimensional reconstruction of the discharge chan-
nel. This paper will detail a laboratory investigation into 
the reconstruction of high voltage discharge channels, 
with the intention of expanding to field experiments with 
natural or triggered lightning attachment to a tall tower. 
Modifications of an existing three-dimensional recon-
struction method will be presented for the channel re-
construction [4-5]. 
This work investigates the challenge of reconstructing a 
three-dimensional channel using optical cameras record-
ing at different elevations. This is a preliminary investiga-
tion that looks into the accuracy of the algorithm used to 
normalize images at elevation to an eye-level approxima-
tion. 
 
2 - BACKGROUND 
 
A 250 m tall tower, namely Brixton Tower, is situated in 
Johannesburg, South Africa and is being monitored for 
lightning activity through photographic surveillance [6]. 
Additional perspectives will be set up to provide the 
depth perception required for three-dimensional recon-
struction. 
 
Figure 1 shows the expected scenario for obtaining opti-
cal lightning data striking Brixton Tower. There are two 
prospective recording sites for photographing lightning 
flashes to Brixton Tower from different perspectives. 
There is an approximate 70º lateral angular separation 
between the two sites, which should provide significant 
depth perception for three-dimensional reconstruction. 
Although the sites provide appropriate depth perception, 
the locations of these two sites would present some diffi-
culties for reconstruction, as Site 1 is approximately eye-
level, whereas Site 2 has a large acute angled perspec-
tive. 
 
 
Figure 1: The camera placement expected for lightning channel 
reconstruction of lightning strokes occurring on Brixton Tower. 
Associated heights, distances and expected angular elevations 
are included. 
Eye level
Zenith
20°
50°
40°
70°
Camera 
Elevation 
Range
 
 
Figure 2: Camera elevation range to the discharge channel with 
respect to the zenith – angles ranging from 40°-70° . In this ex-
ample, a rod-to-rod gap configuration is used.  
 3 - BASIC CONSIDERATIONS 
 
A laboratory investigation is essential to evaluate the 
effectiveness of reconstructions with cameras at different 
elevations before reconstructing lightning channels on a 
large-scale setup. The investigation simulates the ex-
pected channel reconstruction challenge of differing 
camera elevations, and therefore evaluating the three 
dimensional algorithm for this scenario. High voltage 
discharge channels were created a rod-to-rod gap confi-
guration. The expected channel length for this investiga-
tion was approximately 0.66 m. 
 
3.1 - CAMERA CONSIDERATIONS 
 
The use of three surveillance cameras was intended for 
the laboratory testing. The test configurations were de-
fined to provide a preliminary evaluation of the effective-
ness of the three-dimensional reconstruction algorithm. 
The two cameras used were of the same model, which 
have a motion detection triggering mechanism and an 
image pre-buffer. The cameras were placed 2 m away 
from the discharge channel, which is relatively close 
range and therefore optical filters were used for each 
camera to dampen the intensity of the channel. 
 
3.1 - CAMERA PLACEMENT 
 
There were two tests that were implemented: Mirrored 
test (cameras placed at 180º separation) and 90º sepa-
ration test. Each of these tests had one camera at eye 
level, while the height of the second camera varied in 
each scenario, as provided in Table 1. These heights do 
not provide a zenith angle up to 40º which is the angle 
required for Site 2 from Figure 1. The zenith angles pro-
vided in Table 1 will provide a proof of concept for the 
elevation reconstruction method. For the consistency 
through this paper, Camera 1 was defined as the refer-
ence camera, at 0° and 0 cm elevation. Camera 2 was 
varied accordingly. 
 
Table 1: Camera height variations and the corresponding eleva-
tion angles. 
Height below 
eye level (cm) 
Elevation Angle 
(α) 
Zenith Angle  
(β) 
18.00 5.14º 84.82º 
35.26 10º 80º 
65.00 18º 72º 
The mirrored test provides a quantifiable comparison for 
a channel path that is always random. Twelve samples of 
the mirrored test with the cameras both at approximately 
eye-level were obtained. A further five samples were 
taken of each varied height from Table 1 of one camera. 
General error trends will be used to determine the effec-
tiveness of the modified algorithm which will account for 
cameras at different elevations. 
 
4 – THREE-DIMENSIONAL RECONSTRUCTION 
 
The three-dimensional reconstruction method illustrated 
in Figure 3 was developed by Liu and Rapson in 2008 
[4]. The algorithm that reconstructed three-dimensional 
models of high voltage channels assumed that the cam-
eras photographed images of equal elevation from two or 
three perspectives. Liu later reconstructed lightning 
channels attaching to Brixton Tower with only one cam-
era perspective, by using a mirrored image and a white 
straight-lined image in the three-dimensional environ-
ment [5]. This method, illustrated in Figure 3, successful-
ly reconstructed a two-dimensional branched lightning 
channel in an interactive three-dimensional environment. 
A revision of this algorithm must be considered to ac-
count for multiple captured photograph perspectives from 
cameras located at different elevations. 
 
4.1 – RECONSTRUCTION METHOD 
 
The images taken from the test setup were filtered to 
Boolean black and white images using Liu and Rapson’s 
three-dimensional reconstruction application. This was 
necessary for the reconstruction application to clearly 
identify the discharge channel information from the im-
age, and remove any grey-scale ambiguity. Figure 4 (a) 
and (b) provide an example of a photograph taken of a 
discharge channel which is filtered to black and white 
Boolean pixels, removing any grayscale ambiguity for the 
channel information. Figure 4 (c) shows an image of the 
rendered model. This image is taken at the same angular 
separation as the test environment of the camera. Figure 
4 (d) follows the example into the testing stage, which 
provides the pixel mismatch indicated by the white pixels. 
These pixels are counted by a tester application, which 
provides the value for the ε parameter in Equation (1). 
The example provided in Figure 4 was an image taken 
from Camera 2 at eye-level (0 cm elevation). 
 
y
xz
 
Figure 3: Example of reconstruction of mirror-image a test using 
the existing algorithm for three-dimensional reconstruction of 
eye-level camera perspectives. This shows the projection of 
normals from white pixels to the center; intersections define the 
discharge channel. 
 
 
  
 (a) (b) (c) (d) 
Figure 4: An example of the testing process from Camera 2 
(a) Original image (b) Digitally filtered black and white Boolean 
image (c) Rendered model (d) Pixel mismatch of (b) and (c). 
 Figure 5: Results obtained from the mirrored test to obtain a 
percentage mismatch for each camera and each elevation test. 
 
Figure 6: Results obtained from the 90° separation test to obtain 
a percentage mismatch for each camera and each elevation 
test. 
 
5 – TESTING 
 
Although the mirrored tests cannot provide any three-
dimensional definition, it has value in determining the 
accuracy of image data that is obtained. Reconstructing 
high voltage channels from these tests would require the 
implementation of Liu’s method mentioned in Section 4 
and illustrated in Figure 3. 
 
The model accuracy was determined using a tester ap-
plication that compares the pixel mismatch of two given 
images [4-5]. A percentage mismatch is determined us-
ing Equation (1), where ε is the pixel mismatch deter-
mined by the tester application, h and w account for the 
height and width of the tested image in pixels. The tester 
application requires identical image sizes, so there could 
only be one value for h and w. 
 
100% ×
×
=
wh
error
ε
 
 
(1) 
 
The error calculation may provide a misleading result, as 
it takes into account the total error of the entire image, 
and not only of the significant channel information. There 
were a few reasons that may have accounted for the 
error: the thickness of the channel did not match; and the 
image of the model was slightly off-centered, providing a 
mismatched image for comparison. 
 
Ten samples were taken of the mirrored test with both 
cameras at the same elevation. All subsequent test con-
figurations had five samples recorded. 
 
6 – RESULTS 
 
Figure 5 and Figure 6 provide the resulting average 
trends obtained for the mirrored and 90° separation test 
from the values shown in Table 2. 
 
The test results would show a larger percentage error for 
the test with Camera 2 at the lowest elevation if camera 
elevation plays a significant role in the reconstruction 
process. From Table 2, the results from Camera 2 ap-
peared to provide an accurate description of what would 
be expected for the mirrored tests. There is a steady 
upward trend to higher percentage mismatches to the 
digitally filtered image, and the image taken from the 
reconstructed model. This expectation breaks down for 
each of all other scenarios, and the consistency of Cam-
era 2 is questioned with a resulting trend for the 90° se-
paration test that reverses the original expectation. 
 
The large percentage errors obtained from Camera 1 
may be attributed to its higher light sensitivity than that of 
Camera 2, which was evident in each of the photographs 
taken for each test. Although the cameras are identical, 
with the use of identical optical filters and equal radial 
placements from the discharge channel, the cameras 
had both been used for different surveillance periods 
preceding these experiments. 
 
The consistent results from Camera 1 can be considered 
as a correct representation of what may be expected in 
the larger scale scenario, as the largest angle of eleva-
tion (referred to α as in Figure 1) of 18°. Tests using 
more extreme angles of elevation need to be performed 
to provide any conclusive comments. 
 
The example of a reconstructed discharge channel in 
Figure 4 (a) demonstrates how inconsistencies from 
simple tests can be identified. The modeling algorithm 
used for this channel uses first edge detection [4]. This 
produces a segment of the channel whenever normals 
meet (demonstrated in Figure 3). It is evident that there 
are two channels created over one another; the one in 
front appearing to be shorter in length. This presents the 
need for preprocessing the image data possibly by scal-
ing the smaller image. This inconsistency may occur 
from the curvature of the camera, imperfect camera 
placements and non-specific filtering schemes for differ-
ent light intensities. 
 
Table 2: Averaged percentage errors for each discharge chan-
nel reconstruction test for cameras located at different eleva-
tions, using the percentage error calculation presented in Equa-
tion (1). Camera 1 is placed at 0 cm elevation for each scenario. 
Percentage error for each test (%) 
Camera 2 
Elevation 
(cm) 
Mirrored Test 90° Separation Test 
Camera 
1 
Camera 
2 
Camera 
1 
Camera 
2 
0 9.59* 2.61* 8.92 4.70 
-18 7.25 7.12 8.02 1.96 
-35 8.06 9.91 8.49 0.84 
-65 7.43 12.57 13.87 0.14 
* Ten samples were taken for the mirrored test at cameras of 
equal elevation. Five samples were taken for all other scena-
rios. 
  
Figure 7: An example of a three-camera configuration for photo-
graphing the high voltage discharges in terms of angular separa-
tion and elevation. 
 
Figure 8: Image eye-level normalization method for an image 
taken at a different elevation.  
 
7 - DISCUSSION 
 
It can be seen from the results that the use of identical 
cameras (and setup) can still provide inconsistencies in 
the reconstruction of discharge channels. These incon-
sistencies can be addressed through modification of the 
reconstruction system (which may include a reassess-
ment of the algorithm used). 
 
7.1 – THREE CAMERA CONFIGURATION 
 
A more comprehensive laboratory test will be performed 
with the availability of a third camera. Several camera 
placement configurations will be considered for a 
branched discharge channel, which will provide a proof 
of concept for a more accurate representation of upward 
lightning that occurs from Brixton Tower. Examples are 
shown in Figure 2 and Figure 7. In particular: 
1. A reference Camera 1 will be placed at eye-
level to the high voltage discharge channel, at 
0º separation). 
2. A lower elevation Camera 2 will be placed be-
low eye-level with zenith angles (β) ranging from 
40º - 70º. This camera will also be varied later-
ally (θ) from 30°-90° separation from Camera 1. 
3. An eye-level mirrored Camera 3 will be placed 
180° from Camera 2 for eye-level normalization 
comparison. 
 
7.2 – MODIFICATIONS FOR CAMERA ELEVATIONS 
 
The easiest way to account for images taken from differ-
ent camera elevations would be to normalize the images 
to eye-level as shown in  
Figure 8. This would avoid any unnecessary modification 
to the existing modeling algorithm. Since this method is 
based on pixels, it may present resolution problems for 
the normalized image. 
 
Once the image is normalized to eye-level, it can be 
compared with the mirrored eye-level image in order to 
test the accuracy of the normalization method. 
 
7.3 – LARGE SCALE EXPERIMENTS 
 
Liu successfully reconstructed two-dimensional branched 
lightning channel models using one camera perspective 
into a three-dimensional interactive environment using 
Liu and Rapson’s reconstruction application [5]. This 
work has shown that discharge channel reconstructions 
can be accomplished for small elevation angles without 
any modification to the reconstruction algorithm. With the 
ground work set in place, large scale reconstructions will 
be attempted for lightning attachment to Brixton Tower. 
 
7 - CONCLUSION 
 
This investigation has shown that elevation angles be-
tween 0° and 18° have inconclusive results. Camera 2 
has provided an expected trend in one of the test confi-
gurations by increasing the pixel mismatch according to 
a greater angle of elevation. Camera 1 provided a mostly 
random trend, which may suggest that the elevation an-
gles are too slight to show any significant difference. 
Tests using the modification method mentioned in Sec-
tion 7.2 may provide more conclusive results. 
 
The use of a third camera will provide an extra reference 
point to the random shape of the high voltage discharge 
channel; although this may even present more inconsis-
tencies to the reconstruction. 
 
Identical camera setups may still introduce inconsisten-
cies into the discharge channel reconstructions. More 
preprocessing steps need to be taken to reduce the re-
sulting errors from the image data inconsistencies. 
 
8 – ACKNOWLEDGEMENTS 
 
The authors would like to thank CBI-electric for funding 
the Chair of Lightning at the University of the Witwater-
srand and for direct support of the Research Group. 
They would also like to thank Eskom for the support of 
the Lightning/EMC Research Group through the TESP 
programme. Thanks are extended to the department of 
Trade and Industry (DTI) for THRIP funding as well as to 
the National Research Foundation (NRF) for direct fund-
ing of the Research Group. 
 
9 - REFERENCES 
 
[1] Eriksson, A.J., “Lightning and Tall Structures”, The Trans-
actions of the SA Institute of Electrical Engineers (SAIEE), 
1987. 
[2] Cummins, K., Saba, M.M.F., Warner, T.A., Weidman, C., 
Campos, L.Z.S, Fleenor, S.A., Saraiva, A.C.V., Scheftic, 
W.D., “A Multi-Camera High-Speed Video Study of Cloud-
to-Ground Lightning in South Arizona --- Preliminary Re-
sults”, International Conference on Lightning Protection 
(ICLP) – Uppsala, Sweden, vol. 29, no. 1c1, 2008. 
[3] Asakawa, A., Miyake, K., Yokoyama, S., Shindo, T., Yoko-
ta, T., Sakai, T., “Two Types of Lightning Discharges To a 
High Stack on the Coast of the Sea of Japan in Winter”, 
IEEE Transactions on Power Delivery, vol. 12, no. 3, pp 
1222-1231, 1997. 
[4] Liu, Y.C., Rapson, A.J., Nixon, K.J., “Laboratory Investiga-
tion into Reconstructing a Three Dimensional Model of a 
Discharge Channel using Digital Images”, South African 
Universities’ Power Engineering Conference (SAUPEC) – 
Stellenbosch, South Africa, vol. 18, pp 18-23, 2009. 
[5] Liu, Y.C., Nixon, K.J., “A Preliminary Investigation into 2D 
Reconstruction of Branched Lightning Discharge Channels 
in a 3D Environment”, South African Universities’ Power 
Engineering Conference (SAUPEC) – Johannesburg, 
South Africa, vol. 19, Paper G-2, pp 295-299, 2010. 
[6] Liu, Y.C.J, Hunt, H.G.P, Grant, M.D., Nixon, K.J., “Obser-
vations of Lightning Discharges on Brixton Tower”, Interna-
tional Conference on Lightning Protection (ICLP) – Cagliari, 
Italy, vol. 30, no. 1073, 2010. 
 
Main author 
Name: Yu-Chieh (Jessie) Liu 
Address: School of Electrical and Information Engineering, Uni-
versity of the Witwatersrand, Johannesburg, 2050, South Africa 
Fax: +27 11 403-1929; Phone: +27 11 717-7201 
E-mail:  Yu-Chieh.Liu@students.wits.ac.za 
 
 
136
Appendix F
Preliminary Testing on One Image
Perspective of Lightning
F.1 Preamble
This appendix is a paper that was accepted and presented for publication by the
South African Universities’ Power Engineering Conference (SAUPEC) in 2010,
hosted in Johannesburg, South Africa. The paper is entitled: A Preliminary
Investigation into 2D Reconstruction of Branched Lightning Discharge
Channels in a 3D Environment .
F.2 Paper Description
The paper describes the results for reconstruction testing of actual lightning events.
This mainly tests the modelling framework’s ability to reconstruct models from
actual lightning pictures that incorporate branching of the channel, thus producing
2D reconstructed models within a 3D environment.
A PRELIMINARY INVESTIGATION INTO 2D RECONSTRUCTION
OF BRANCHED LIGHTNING DISCHARGE CHANNELS IN A 3D
ENVIRONMENT
Y.C. Liu and K.J. Nixon
Dept. of Electrical and Information Engineering, University of the Witwatersrand, Johannesburg, South Africa
Abstract. The study of lightning models provides insight into understanding the behaviour of the natural
phenomenon. By producing 3D lightning models, a greater understanding of the spatial propagation of a lightning
channel can be obtained. A preliminary study was performed to determine whether branched lightning channels
could be modelled from one photograph in a 3D environment. Photographs of lightning strikes were obtained using
Axis 207 surveillance cameras. Cross-polarised optical filters were used to limit the captured light intensity of
the strike. The digital images captured from the cameras were processed manually using an image editor. Three
images were used to create a model; the orginal image, a white straight-line image and a mirrored image of the
original. These images were placed with 90◦ separation in the 3D environment. Fourteen branched models were
reconstructed. An average error of 1.68% was calculated for an image comparison between the filtered image and
a model image. This paper extends on work performed by Liu and Rapson in 2008.
Key Words. 3D reconstruction model, branched lightning channels, lightning photography, image processing.
1. INTRODUCTION
L IGHTNING models form the basis of researchinto further investigating the physical behaviour
of the natural phenomenon [1]. By obtaining a three
dimensional (3D) representation of a lightning dis-
charge, the channel can be properly analysed in a
3D visualised space. A system was implemented to
capture two dimensional (2D) images of a discharge
channel and represent the lightning discharge as a
3D model. Liu and Rapson designed, developed and
implemented a preliminary system [2], which was
tested primarily using single-channelled high voltage
discharges in a controlled laboratory environment.
This paper extends their work, by testing the mod-
elling capabilities of branched lightning channels.
This paper provides an overview of the modelling
procedure; from photographing the lightning chan-
nels, to creating the models in a 3D environment.
Examples are provided for each stage using one
model dataset. Five models are presented to provide
a variation of results.
2. PROBLEM STATEMENT
The nature of lightning occurrences is studied to
broaden the understanding of the lightning mecha-
nism. This knowledge provides a beneficial contri-
bution to lightning protection systems and further
understanding the nature of this phenomenon. Light-
ning protection becomes evident with a cloud-to-
ground (CG) strike with the potential to cause damage
to electrically sensitive devices, power distribution
lines and even structural buildings [3]. The physical
distribution of lightning events is typically considered
using photography of the discharge channel from a
single perspective. This solution lacks the ability to
fully grasp the spatial propagation of the channel,
which highlights a need to develop a system that is
capable of reconstructing a discharge channel within
3D space. The reconstruction must ultimately be able
to determine the channel’s directional data and distin-
guish between split branches. By constructing a 3D
model of a discharge channel, a better understanding
of how the path of a large channel or lightning strike
develops its pattern.
3. BACKGROUND
The difficulties involved with the photography of
lightning, and a brief summary of the 3D modelling
solution developed by Liu and Rapson will be briefly
discussed.
3.1 Photography of Lightning:
The basis of modelling a lightning discharge requires
photographs of the channel. The difficulties involved
with capturing images of a lightning strike include:
the flash duration and the unpredictability of the oc-
currence. For research purposes, it is difficult to verify
whether the correct data of the channel is captured on
the photograph. There are several research solutions
to the photographing lightning channel attachments
to tall structures, such as studies performed on the
Fukui Chimney in Japan [4], CN Tower in Toronto,
Canada [5] [6] [7]. These papers investigate lightning
attachments to tall structures using digital images
from conventional video cameras, or high-speed cam-
eras. These studies provide valuable insight into the
photography of lightning discharges. No mention of
a 3D model is included in these papers, although
some produce images from multiple capture devices
to provide a sense of spatial distribution. Cummins
et al provide preliminary experimental results that
could ultimately lead to producing a time-resolved
3D model of CG lightning discharges [8].
3.2 Liu and Rapson’s Solution
The 3D reconstruction of general high voltage chan-
nels provides insight into their formation, and ulti-
mately its spatial propagation.
yx
z
(a) (b)
Fig. 1: A basic representation of the reconstruction method (a) 3D
reconstruction algorithm (b) A 2D representation of the algorithm
using cylinders for modelling [2].
Liu and Rapson devised a method of recreating the
laboratory scenario in a software application, extend-
ing normals from the image to the central y-axis,
and creating a pixel-high cylinder where the normals
meet [2]. Figure 1 (a) and (b) illustrate a simplified
representation of the algorithm functionality. The
system produces a 3D model of a discharge chan-
nel samples from in a controlled environment. They
focused on reconstructing unbranched high voltage
channels in a laboratory environment. This modelling
algorithm provided a total error of 11% from 70 tests,
through the comparison of the filtered image to an
image of the model from the same perspective.
4. SYSTEM OVERVIEW
The system developed by Liu and Rapson [2] was
modified to account for a physical investigation,
which is the focus of this paper. The physical inves-
tigation considers a discharge environment in a real-
world scenario, which includes the capturing of image
test data from lightning strikes. The system described
in Figure 2 will attempt to render an accurate 2D
model of the channel in 3D space. The following lists
a summary of the system and contents of this paper.
1) The discharge environment is selected to pro-
vide image samples of the lightning strikes.
2) The method of acquiring photographs, and op-
timising the data is discussed.
3) The image processing required for reconstruct-
ing the model is demonstrated, including the
data filtering and description of the algorithm
used.
4) An example of the reconstructed model will be
presented with a discussion on the modelling
capabilities.
5) The testing framework and the sampled results
will be presented and discussed.
5. DISCHARGE ENVIRONMENT AND DATA
ACQUISITION
The test data was taken in the late thunderstorm
season in Johannesburg, South Africa. The reason
for obtaining test data in this location was due to its
high ground flash density. The capture of image data
includes the consideration of the devices used and
optical filters required. Figure 3 displays a set of test
images resulting from this stage. The images provide
a time-resolved lightning strike with multiple strokes.
This would provide a scope for future reconstruction
of time-resolved models.
(a) (b)
Fig. 3: Consecutive images with 10 ms time separation taken of
a cloud-to-cloud (CC) lightning strike.
The camera used for digital capture was the
Axis 207W wireless surveillance IP camera [9]. The
camera was set according to the settings as demon-
strated in Table 1. These were chosen as per the
implemented system in [2].
Table 1: Camera configuration for the physical investigation.
Parameter Value
Frame rate (fps) 15
Pre-Buffer (s) 2
Resolution (pixels) 640× 480
Colour Grayscale
Triggering method Motion detection
Captured images require the data of only the in-
tense light of the discharge channel. For the pur-
pose of the experiment, only wavelengths of the
visible light spectrum were desired for modelling the
discharge [10]. The insignificant data needed to be
filtered out. Optical filters were required to obtain the
usable data in the images. A combination of cross-
polarised filters and camera configurations provided
images that could be used for the reconstruction. The
images in Figure 4 demonstrated the different varia-
tions in the captured images using different layers of
optical filters. A disadvantage to using optical filters
is the possible loss of image detail brought about by
damaged lenses but this is neglected for the purpose
of this experiment.
Discharge 
Environment
Data 
Acquisitioning
Data
Conditioning
Reconstructed 
Model
- Live Lightning Events - Capture Devices
- Data Filtering: Optical
- Data Filtering: Digital
- Algorithm
- 3D Environment
Testing 
Framework
- Image Comparison
Fig. 2: Block diagram demonstrating the expected system overview and flow.
(a) (b)
Fig. 4: Different images taken with and without filters. (a) No
filters (b) Cross-polarised filters.
Figure 4 (a) shows the image captured of a lightning
discharge channel without optical filters. It is ob-
served that the image is extremely overexposed. Two
linearly polarised lenses are placed perpendicularly
to construct a cross-polarised filter, which reduces
the intensity of light entering the lens. The image
captured from this filter is illustrated in Figure 4 (b).
6. DATA CONDITIONING
The images needed be to filtered further so the
channel information could be isolated. Due to the
greyscale ambiguities from the photographed images,
digital filtering was required. Once the images were
filtered to explicit black and white images, the rel-
evant data was extrapolated from the images and
conditioned to provide a reconstructed model.
6.1 Data Filtering: Digital
The application requires black and white images to
extract the relevant data points from the image. The
white pixels represent the channel information, and
the black pixels are ignored. The digital filtering pro-
vides a means to isolate the channel information. The
images were manually processed, and then filtered
again in the application. This may seem ambiguous,
but the purpose of manually filtering the images
ensured that the less pronounced branches in the
channel were portrayed in the model. The filtering in
the application just ensures that the inserted images
have usable data.
(a) (b)
Fig. 5: Manually processed images taken of lightning strike.
The images in Figure 5 depict the result of manually
filtering the photographs from Figure 3, using an im-
age editor. These images were overlayed and amalga-
mated to combine the discharge channel information,
as shown in Figure 6. Each of these images can be
used as individual test samples.
Fig. 6: Amalgamated lightning strike from individual images.
The images were inserted into the modelling frame-
work in the preparation of data conditioning. The
filtering process includes a tracking function, to de-
termine the relevant channel information from the
image, and crops it to a smaller size, to decrease the
processing time of the reconstruction.
6.2 Algorithm
The 3D algorithm was written in C++ programming
language, integrated with VTK — an open source,
cross-platform visualisation toolkit. The application
could reconstruct a model using two or three im-
ages; each configuration may have different options
for reconstruction. Using the VTK 3D environment,
the filtered images were arranged on a set of axes
in 3D space, mapping the experimental setup. The
algorithm was designed to process the setup in layers
over the y-axis. This method eliminated the third
dimension, reducing the algorithm to a 2D problem,
as demonstrated in Figure 1. Normals of the white
segments were projected to the centre of the setup,
where they were compared to the normals from other
perspectives. Each layer of the discharge was assumed
to have a cylindrical body. The centres of two images
determined the centre point of the cylinder, where the
average thickness of the images determined the radius
of the cylinder. The third image was used to verify
the existence of the cylinder.
y
xz
Fig. 7: Algorithm for one image reconstruction.
Since only one image perspective was taken per
lightning strike, it was expected that the model could
not have any 3D definition. Thus, a white straight-
line image was placed 90◦ from the original image, as
depicted in Figure 7. Due to algorithm limitations for
two images, the split branches in the channel were not
accounted for, and only the main channel at which the
points intersected was modelled. This was resolved
by using three images place with a 90◦ separation.
The third image was created using the image editor
to provide a mirrored imaged of the original. This
was placed 180◦ from the original image to identify
the channel branching.
7. MODEL
Fourteen models were constructed using test data ob-
tained in the physical investigation. Figure 8 provides
an example of the models that were created. A visual
comparison of the model with the filtered image used
for the reconstruction is presented. The image of
the reconstructed model was taken from the same
perspective as the filtered image for the appropriate
comparison.
(a)
(b)
Fig. 8: Filtered image (a) compared to reconstructed model (b).
It can be observed that the algorithm is not perfect,
and does not flawlessly reconstruct the channel path,
even with the ambiguity of the mirrored image. The
reconstruction seems to break down when the channel
thickness thins in the path. This could be explained
by the fact that the original image and the mirrored
image do not get perfectly aligned to receive the
logical identifier as an indication that a cylinder
exists. This property is confirmed in some of the
other samples which produce continuation of thicker
channels and corresponding paths.
8. TESTING AND RESULTS
In order to quantitatively verify the model accuracy,
the images in Figure 8 were compared using a tester
application. An image difference in pixels was pro-
duced, identifying the pixel mismatch between the
two images. Equation 1 provides the error calculation
for the model verification, where ε is the pixel mis-
match determined by the tester application, h and w
account for the height and width of the tested image
in pixels.
% error = εh× w × 100 (1)
Table 2: Testing information for model
Parameter Value
Image difference ε 321.51
Height h (pixels) 500
Width w (pixels) 160
Percentage Error (%) 0.40
There could only be one value for h and w, since
the tester application requires identical image sizes.
The error calculation takes into account the total error
of the entire image, and not only of the significant
channel information. This may provide a misleading
result, since the calculation is a function of the image
size (which includes the redundant black pixels).
Equation 1 presents an error of 0.40% for the created
model in Figure 8 using the information in Table 2.
All fourteen samples were tested with the results
provided in Figure 9 with an average error of 1.68%.
It should be noted that Model 1 in Figure 9 is the
model demonstrated as the running example within
this paper. The error ranges from 0.16 to 8.47%,
which is a considerably large range and could be
accounted for by several different factors. There were
a few things that specifically accounted for the error:
the thickness of the channel did not match; there were
missing links in the channel path; and the image
of the model was slightly off-centred, providing a
mismatched image for comparison.
1 2 3 4 5 6 7 8 9 10 11 12 13 14
0
1
2
3
4
5
6
7
8
9
Model Number
Pe
rce
nta
ge
 Er
ror
 (%
)
Fig. 9: Results for error calculation of branched test models.
It was only possible to determine the error of the
filtered image to the image acquired from the model
from the same perspective. Other errors occuring in
the system that should be taken into account, but
could not be quantified include: lightning to optically
filtered images, optically filtered images to manually
filtered images, manually filtered images to applica-
tion filtered images.
9. ANALYSIS
The models of fourteen datasets were successfully
reconstructed. The models provided an average error
in comparison to the filtered images of 1.68%, even
though the error calculation has been identified as
being misleading. Also, the cylinder radius for the
channel was determined by the thickness of the
straight-line image placed 90◦ relative to the lightning
image, which could account for the inaccuracies of
the model thickness. This work presents the first
recorded testing data of the algorithm using branched
channels acquired from a physical investigation. The
full system error could not be easily quantified.
The average error of the high voltage discharges from
[2] can be seen to differ by an order of magnitude
to the average error obtained in the physical investi-
gation of this paper. This could be accounted for by
several factors from the laboratory investigation: more
tested datasets and a combination of the different
algorithm configurations (differing when using 2 or
3 images), more images with possible inaccurate
angular placements in the environment setup.
10. FUTURE WORK
More models need to be reconstructed and tested
for the physical investigation in order to provide a
better perspective on the algorithm performance. This
will also provide better comparisons to the test data
obtained from the experimental investigation.
A detailed testing platform needs to be established,
taking into account only the significant information,
instead of testing the entire image. This includes
determining the reason for the offsetted image of the
model for error comparison, thus providing a better
means for comparison. Currently, a more comprehen-
sive testing framework is being developed. This test
would compare two images with a branched channel
which would determine the points of branching and
channel path termination. This would map out the
position of the points in question and compare the
number of significant points and accuracy of the
image of the reconstructed model.
Of course, this paper provides a proof of concept to
obtaining 3D models of lightning discharges. This
provides a platform for reconstructing the lightning
models using multiple-perspective images of a strike.
This would require a scaled version of the work
performed in [2].
11. CONCLUSION
This paper presented a preliminary investigation into
considering the plausibility of modelling a 2D light-
ning image in a 3D environment. It has been shown
that it is possible to capture lightning images us-
ing an Axis 207 surveillance camera with a cross-
polarised optical filter. The channel information was
extracted from the image using manual and applica-
tion filtering. Fourteen branched discharge channels
were successfully modelled using three images per
photograph. The algorithm configuration using three
images with a 90◦ -separation provided an error of
1.68% from fourteen test models. A comprehensive
testing method needs to be developed to obtain a more
accurate error calculation. Additional test data needs
to be obtained in order to provide more models for
comparison. And lastly, this proves that in theory, by
scaling the system in [2], a 3D model of a branched
lightning channel can be obtained.
REFERENCES
[1] V. Rakov and M. Uman. Lightning — Physics and Effects.
Department of Electrical and Computer Engineering, Univer-
sity of Florida: Cambridge University Press, 2003.
[2] Y. Liu, A. Rapson, and K. Nixon. “Laboratory Investi-
gation into Reconstructing a Three Dimensional Model of
a Discharge Channel using Digital Images.” SAUPEC —
Stellenbosch, South Africa, vol. 18, p. 83, 2009.
[3] S. Prentice and R. Golde. Lightning Volume 1: Physics
of Lightning — Frequency of Lightning Discharges, chap.
100, pp. 100–100. Department of Electrical Engineering,
University of Queensland, Brisbane, Australia: Acedemic
Press Inc., New York, 1977.
[4] M. Miki, A. Wada, and A. Asakawa. “Observations of
Upward Lightning in Winter at the Coast of Japan Sea with
a High-speed Video Camera.” ICLP — Avignon, France,
vol. 27, no. 1a2, 2004.
[5] A. Hussein, W. Janischewskyj, F. Noor, and M. Milewski.
“Characteristics of Lightning Flashes Striking the CN Tower
below its Tip.” ICLP — Avignon, France, vol. 27, no. 4p8,
2004.
[6] A. Hussein, M. Milewski, A. Abdelraziq, W. Janischewskyj,
and F. Jabbar. “Visual Characteristics of CN Tower Lightning
Flashes.” ICLP — Kanazawa, Japan, vol. 28, no. I-11, 2006.
[7] A. Hussein, V. Todorovski, M. Milewski, K. Cummins, and
W. Janischewskyj. “Characteristics of Lightning Strikes at
and in the Vicinity of the CN Tower.” ICLP — Uppsala,
Sweden, vol. 29, no. 1c4, 2008.
[8] K. Cummins, M. Saba, T. Warner, C. Weidman, L. Campos,
S. Fleenor, A. Saraiva, and W. Scheftic. “A Multi-Camera
High-Speed Video Study of Cloud-to-Ground Lightning in
South Arizona — Preliminary Results.” ICLP — Uppsala,
Sweden, vol. 29, no. 1c1, 2008.
[9] Axis Communications AB. AXIS207 Users Manual Rev 3.0,
August 2006.
[10] R. Serway and J. Jewett. Physics for Scientists Engineers
with Modern Physics. Thomson Bokes/Cole, 6th ed., 2004.
142
Appendix G
Single-channelled Lightning Testing
G.1 Preamble
This appendix is a paper that was accepted and presented for publication by the
International Conference on Atmospheric Lightning (ICAE) in 2011, hosted in Rio
de Janeiro, Brazil. The paper is entitled: A Method of Creating Graphical
Three-Dimensional Reconstructions of Lightning Discharge Channels us-
ing Digital Images.
G.2 Paper Description
This paper briefly describes the reconstruction method and uses lightning image
information from Tuscon USA in 2007 courtesy of Dr Marcelo Saba. Two image
perspectives, separated laterally by approximately 34◦, were taken of the single-
channelled lightning flash, and this paper describes the reconstruction process of
the flash in question.
XIV International Conference on Atmospheric Electricity, August 08-12, 2011, Rio de Janeiro, Brazil 
 
A Method of Creating Graphical Three-Dimensional 
Reconstructions of Lightning Discharge Channels using 
Digital Images 
Y.C. Liu1, K.J. Nixon1, I.R. Jandrell1  
 
1. School of Electrical & Information Engineering,  
University of the Witwatersrand, Johannesburg, South Africa 
 
ABSTRACT: This paper describes a method used for graphically reconstructing three-dimensional lightning 
channels within an interactive virtual environment. Typically, lightning is optically observed using one or two 
perspectives of a specific stroke or flash. Two camera perspectives provide depth to the channel that one 
perspective lacks, but these are limited to an ability to discern the contents. This work provides the possibility of 
studying a lightning discharge channel from an actual event in the form of a reconstructed model with the ability 
to zoom, tilt and rotate the channel within a three-dimensional environment. 
 
1. INTRODUCTION 
Lightning models form the basis of research into further investigating the physical behaviour of the natural 
phenomenon [Rakov and Uman, 2003]. By obtaining a three-dimensional (3D) representation of a lightning 
discharge, the channel can be properly analysed in a three-dimensional visualised space. A system was 
implemented to capture two-dimensional (2D) images of a discharge channel and represent the lightning 
discharge as a three-dimensional model.  
 
2. PROBLEM STATEMENT 
Lightning research started with ground-level observations [Malan, 1963]. These fast, almost instantaneous 
events with µs durations were recorded in a two-dimensional capacity with standard camera technology. The 
physical distribution of lightning events is typically considered using photography of the discharge channel from 
a single perspective. This limitation leads to some critical assumptions about the nature of lightning channel 
propagation which become translated to theoretical analyses. This solution also lacks the ability to fully grasp the 
spatial propagation of the channel, which highlights a need to develop a system that is capable of reconstructing 
a discharge channel within three-dimensional space. The reconstruction must be able to successfully determine 
the directional data of the channel and distinguish between split branches.
3. SYSTEM OVERVIEW 
A system was designed and developed to reconstruct three-dimensional reconstruction of lightning 
discharges using photographic images coupled with geographical locations of the cameras in relation to the 
lightning termination point. This system was previously tested using single-channeled high voltage discharges in 
a small scale test [Liu et al, 2009; Liu et al, 2010b], and in a lightning environment using one image of a 
branched lightning discharge as a preliminary investigation [Liu and Nixon, 2010a]. Each of these tests proved 
successful in recreating a three-dimensional reconstruction of test images. 
____________________ 
∗ Correspondence to: Yu-Chieh (Jessie) Liu, University of the Witwatersrand, Johannesburg, South Africa. E-mail: yu-chieh.liu@wits.ac.za 
XIV International Conference on Atmospheric Electricity, August 08-12, 2011, Rio de Janeiro, Brazil 
 
2 
 
Figure 1 provides a block diagram representing each stage of the reconstruction process. This paper 
describes an overview of the modelling procedure; from obtaining photographs of the lightning channels, to 
creating the models in a three-dimensional interactive virtual environment.  
 
Figure 1: Overview of the system for the three-dimensional lightning reconstruction application. 
 
3.1 Reconstruction Application 
The application created for the reconstruction of the three-dimensional lightning models was developed in 
C++ using a visualization toolkit library (VTK). The application framework accepts two or three images of the 
same lightning flash from two or more perspectives. The option for two images was developed for 
single-channeled discharges, as branched channels would create ambiguities in the reconstruction. This 
ambiguity was solved by developing an option for three images. The current reconstruction algorithm requires 
image perspectives with a lateral separation of approximately 30º to 150º for optimal reconstruction. 
 
3.1.1. Image Processing 
The reconstruction application identifies the lightning pixel data using a number of built-in automated digital 
filters. These filters replace pixels that represent the lightning flash with white pixels (pixel value of 255), and 
redundant information as black pixels (pixel value of -255). Depending on the quality of the input images, 
manual image processing may be implemented to correctly catergorise ambiguous grey pixels. 
 
3.1.2. Reconstruction Algorithm 
The processed images are placed in the three-dimensional virtual environment, in the corresponding position 
to its original camera position as demonstrated by Figure 2a for 90º camera separations. In this virtual 
environment, the lightning discharge channel is centered about the y-axis (i.e. x = 0 and z = 0).  
The three-dimensional reconstruction algorithm has been simplified to a series of two-dimensional 
geometric problems. For example, consider a single-channeled discharge channel that has two camera 
perspectives demonstrated in Figure 2b. From the first white pixel band at the top of each image, three 
perpendicular normals are extended from each image towards the y-axis. Each normal is extended from a 
specific point in the 1-pixel high band of white pixels. The points are demonstrated in Figure 2b and listed 
below: 
a. Leftmost white pixel 
b. Rightmost white pixel in a continuous band 
c. Middle position between point a. and b. 
 
The middle normals of each image are compared for an intersection. If an intersection between the normals 
exists, a one-pixel high cylinder is created, using the intersection points of the leftmost and rightmost white pixel 
positions to calculate the radius of the cylinder as demonstrated in Figure 2b. This process is repeated to produce 
a reconstructed model that is constructed by a series of stacked cylinders. 
XIV International Conference on Atmospheric Electricity, August 08-12, 2011, Rio de Janeiro, Brazil 
 
3 
 
y
xz
 
(a) 
 
(b) 
Figure 2: A graphical representation of the three-dimensional reconstruction algorithm which reduces the 
problem to a series of two-dimensional geometric solutions. (a) Processed lightning images placed in at positions 
of 90º-separations in a three-dimensional virtual environment with a simple representation of extended normals 
to reconstruct a channel. (b) Overhead two-dimensional perspective with relevant points in a data image 
extending geometric normals towards the y-axis.  
 
3.2 Lightning Image Test Data 
Two perspectives of a lightning flash were recorded in Tuscon USA in 2007 [Saba, 2010]. The cameras 
were positioned at a lateral separation of approximately 34º. The two images can be seen in Figure 3a and 3b. 
 
 
 (a) 
 
(b) 
Figure 3: Lightning images taken in Tuscon USA in 2007 of the same flash from two different perspectives 
approximately 34º apart [Saba, 2010]. (a) Camera 1. (b) Camera 2. 
4. MODEL AND TESTING 
A three dimensional model has been reconstructed using the images in Figure 3a and 3b. The input images 
and resulting model of the reconstruction application is shown in Figure 4. Camera 1 perspective is shown in 
Figure 4a and 4b, and Camera 2 perspective required a manual scaling process and is shown in Figure 4c and 4d. 
The yellow vertical rod is representative of the y-axis mentioned in Figure 2a. 
Visually, it is evident that the reconstructed model correctly follows the path of the lightning channel in the 
image. In Figure 4b, the mid-section is missing some information, and further inspection indicates that the area 
correlates to a very thin channel width in Figure 4a. This has been a common observation from previous tests, 
and is explained by the fact that normals may not be generated if a channel is one-pixel wide. 
XIV International Conference on Atmospheric Electricity, August 08-12, 2011, Rio de Janeiro, Brazil 
 
4 
 
 
(a) 
 
(b) 
 
 (c) 
 
(d) 
Figure 4: Reconstruction model input images and correlating images of outputs. (a) Digitally filtered Camera 1 
image. (b) Three-dimensional reconstruction of Camera 1 image compared to (a) in three-dimensional 
environment. (c) Digitally filtered Camera 2 image. (d) Three-dimensional reconstruction of Camera 2 image 
compared to (c) in three-dimensional environment. 
5. FUTURE WORK AND CONCLUSIONS 
Current work involves the reconstruction of larger data-sets, including branched lightning flashes. 
Furthermore, a testing framework needs to be implemented to accurately quantify the error associated with the 
reconstruction algorithm. A testing framework currently exists, but is based solely on pixel mismatches from 
input and output images, which can be misleading for comparisons of larger images to smaller images. 
The algorithm has been shown to provide successful path reconstructions of single-channeled lightning 
discharge channels, but fails when pixel widths of channels become too thin. Further investigations into solving 
this discontinuity problem will need to be conducted without having to compromise the input image data. 
ACKNOWLEDGEMENTS 
The authors would like to thank Dr Marcelo Saba for providing the lightning image data used in this paper.  
The authors would also like to thank CBI-electric for funding the Chair of Lightning at the University of the 
Witwatersrand and for direct support of the Research Group. They would also like to thank Eskom for the 
support of the Lightning/EMC Research Group through the TESP programme. Thanks are extended to the 
department of Trade and Industry (DTI) for THRIP funding as well as to the National Research Foundation 
(NRF) for direct funding of the Research Group. 
REFERENCES 
Liu, Y.C. Rapson, A.J. Nixon K.J (2009), Laboratory Investigation into Reconstructing a Three Dimensional 
Model of a Discharge Channel using Digital Images, SAUPEC – Stellenbosch, South Africa, Vol. 18 pp. 83 
Liu, Y.C. Nixon, K.J. (2010a), A Preliminary Investigation into 2D Reconstruction of Branched Lightning 
Discharge Channels in a 3D Environment, SAUPEC – Johannesburg, South Africa, Vol. 19 No. G-2 
pp. 295-299. 
Liu, Y.C. Nixon, K.J. Jandrell, I.R. (2010b), Preliminary Investigation into Three-Dimensional Reconstruction of 
Laboratory High Voltage Discharges using Photographs taken from Different Elevation Perspectives, 
Ground LPE – Salvador, Brazil, Vol. 4, No. P8. 
Malan, D.J. (1969), Lightning and its Effects on High Structures, The Transactions of the S.A. Institute of 
Electrical Engineers, vol 60, no. 6, pp 241-242. 
Rakov, V. and Uman, M. (2003), Lightning – Physics and Effects. Department of Electrical and Computer 
Engineering, University of Florida: Cambridge University Press. 
Saba, M. (2010), Personal Communication, Instituto Nacional de Pesquisas Espaciais, Av. dos Astronatuas, 1758 
– 12227-010 – S. José dos Campos/SP – Brazil.