Application of the Topological Gradient Method to Color Image Restoration

作者：Auroux Didier^*; Belaid Lamia Jaafar; Rjaibi Badreddine

来源：SIAM Journal on Imaging Sciences, 2010, 3(2): 153-175.

DOI：10.1137/080721017

• topological gradient
• topological asymptotic expansion
• image restoration
• Di Zenzo gradient
• color vision

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.

• 出版日期2010