Cellular Automata (CA) theory is a discrete model that represents the stateof each of its cells from a finite set of possible values which evolve in timeaccording to a pre-defined set of transition rules. CA have been applied to anumber of image processing tasks such as Convex Hull Detection, Image Denoisingetc. but mostly under the limitation of restricting the input to binary images.In general, a gray-scale image may be converted to a number of different binaryimages which are finally recombined after CA operations on each of themindividually. We have developed a multinomial regression based weighedsummation method to recombine binary images for better performance of CA basedImage Processing algorithms. The recombination algorithm is tested for thespecific case of denoising Salt and Pepper Noise to test against standardbenchmark algorithms such as the Median Filter for various images and noiselevels. The results indicate several interesting invariances in the applicationof the CA, such as the particular noise realization and the choice ofsub-sampling of pixels to determine recombination weights. Additionally, itappears that simpler algorithms for weight optimization which seek local minimawork as effectively as those that seek global minima such as SimulatedAnnealing.
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