Title: Bitwise Operations of Cellular Automaton on Gray-scale Images,
Abstract: Cellular Automata (CA) theory is a discrete model that represents the state
of each of its cells from a finite set of possible values which evolve in time
according to a pre-defined set of transition rules. CA have been applied to a
number of image processing tasks such as Convex Hull Detection, Image Denoising
etc. 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 binary
images which are finally recombined after CA operations on each of them
individually. We have developed a multinomial regression based weighed
summation method to recombine binary images for better performance of CA based
Image Processing algorithms. The recombination algorithm is tested for the
specific case of denoising Salt and Pepper Noise to test against standard
benchmark algorithms such as the Median Filter for various images and noise
levels. The results indicate several interesting invariances in the application
of the CA, such as the particular noise realization and the choice of
sub-sampling of pixels to determine recombination weights. Additionally, it
appears that simpler algorithms for weight optimization which seek local minima
work as effectively as those that seek global minima such as Simulated
Annealing.