Cross-diffusion systems for image processing: I. The linear case

TL;DR

This paper explores linear cross-diffusion systems as models for image processing, identifying key properties and analyzing their effects on filtering through numerical experiments.

Contribution

It characterizes linear cross-diffusion systems that satisfy scale-space properties and studies their impact on image filtering.

Findings

Certain cross-diffusion systems preserve scale-space properties

Numerical results demonstrate the filtering effects of cross-diffusion

The study provides insights into linear cross-diffusion applications in image processing

Abstract

The use of cross-diffusion systems as mathematical models of different image processes is investigated. The present paper is concerned with linear filtering. First, those systems satisfying the most important scale-space properties are identified. Then a numerical study on the effect of cross-diffusion in filtering problems is presented.