Application of the Topological Gradient Method to Color Image Restoration
The aim of this paper is to generalize to color images the topological gradient method for the restoration problem. First, we consider a simple extension from grey-level to color images, by considering a channel by channel method. Then, as there should be some coupling between the different channels, we propose considering a tensorial approach: the Di Zenzo gradient. We derive an asymptotic expansion of this gradient with respect to the insertion of a small crack in the image, and we propose a new algorithm based on the topological gradient for the color image restoration problem. Finally, we illustrate these two approaches with numerical results.
topological gradient image restoration di zenzo gradient topological asymptotic expansion color vision