Syntactic generation of similar pictures

Abstract

Syntactic picture generation is a significant field in mathematics and computer science introduced over three decades ago. Currently, there is interest in research on the syntactic generation of similar pictures as a result of applications that require the use of similar pictures such as visual password systems. However, the problem with many syntactic picture generators currently available is that they generate an infinite number of pictures without considering the similarity between pictures. Addressing this challenge requires methods that can generate in a controlled manner a finite number of pictures, which are similar. This study presents methods of generating in a controlled manner a finite number of pictures that are similar using bag context picture grammars and random context picture grammars. Firstly, we introduce bag context picture grammars and show how we can generate pictures using them. Next, we present three methods of generating in a controlled way a finite number of pictures that are similar by using both bag context picture grammars and random context picture grammars. The first method is limiting the number of refinements (subdividing of a picture into smaller sub-pictures) of pictures that can be produced by a given picture grammar. For this, all pictures generated by the grammar had the same number of refinements while the distribution of colours varied. The second method is limiting the number of refinements of selected sub-pictures of the picture. The last method is a combination of limiting the number of refinements of pictures and selected sub-pictures of the picture. Furthermore, we compared the simplicity of using both bag and random context picture grammars in generating similar pictures. Moreover, we used a mathematical similarity measure (in this case the spatial colour distribution descriptor) to evaluate the performance of the presented methods and the outcome verified that there is an improvement in the similarity of the generated pictures when using the presented methods. We then collected human perceptions on the similarity of generated pictures in an online survey. The results of the survey were used to evaluate whether there is a correlation between human perceptions and the spatial colour distribution descriptor. The results showed that there is a correlation