# Bitwise Operations of Cellular Automaton on Gray-scale Images

## TL;DR

This paper explores the use of cellular automata on gray-scale images by converting them into binary images, applying CA-based denoising, and recombining them using a multinomial regression method, showing promising results against standard denoising techniques.

## Contribution

The paper introduces a multinomial regression based weighted recombination method for binary images processed by cellular automata on gray-scale images, enhancing denoising performance.

## Key findings

- CA invariance to noise realization and pixel sub-sampling
- Simple local minima algorithms perform as well as global minima methods
- Effective denoising of Salt and Pepper noise compared to median filter

## 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.