Bitwise Operations of Cellular Automaton on Gray-scale Images
This work addresses a domain-specific problem in image processing by enabling CA algorithms to handle gray-scale images, though it is incremental as it builds on existing CA methods with a new recombination technique.
The paper tackled the limitation of applying Cellular Automata (CA) to binary images by developing a multinomial regression-based weighted summation method to recombine binary images from gray-scale inputs, specifically testing it for denoising salt and pepper noise and showing competitive results against standard benchmarks like the Median Filter across various images and noise levels.
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.