Cross-Diffusion Systems for Image Processing: I. The Linear Case

Abstract

The use of cross-diffusion problems as mathematical models of different image processes is investigated. Here the image is represented by two real-valued functions which evolve in a coupled way, generalizing the approaches based on real and complex diffusion. The present paper is concerned with linear filtering. First, based on principles of scale invariance, a scale-space axiomatic is built. Then, some properties of linear complex diffusion are generalized, with particular emphasis on the use of one of the components of the cross-diffusion problem for edge detection. The performance of the cross-diffusion approach is analysed by numerical means in some one- and two-dimensional examples.