Evolution of Cellular Automata with Conditionally Matching Rules for Image Filtering

We present an evolutionary method for the design of image filters using two-dimensional uniform cellular automata. Specifically, a technique called Conditionally Matching Rules is applied to represent transition functions for cellular automata working with 256 cell states. This approach allows reducing the length of chromosomes for the evolution substantially which was a need for such high number of states since the traditional table based encoding would require enormous memory space. The problem of removing Salt-and-Pepper noise from 8-bit grayscale images is considered as a case study. A cellular automaton will be initialised by the values of pixels of a corrupted image and a variant of Evolution Strategy will be applied for the design of a suitable transition function that is able to eliminate the noise from the image during ordinary development of the cellular automaton. We show that using only 5-cell neighbourhood of the cellular automaton in combination with conditionally matching rules the resulting filters are able to provide a very good output quality and are comparable with several existing solutions that require more resources. Moreover, the proposed evolutionary method exhibits a high performance which allows us to design filters in very short time even on a common PC.