UPThèses

English

Extension of the multi-resolution analysis for color images by using graph transforms

In our work, we studied the extension of the multi-resolution analysis for color images by using transforms on graphs. In this context, we deployed three different strategies of analysis. Our first approach consists of computing the graph of an image using the psychovisual information and analyzing it by using the spectral graph wavelet transform. We thus have defined a wavelet transform based on a graph with perceptual information by using the CIELab color distance. Results in image restoration highlight the interest of the appropriate use of color information. In the second strategy, we propose a novel recovery algorithm for image inpainting represented in the graph domain. Motivated by the efficiency of the wavelet regularization schemes and the success of the nonlocal means methods we construct an algorithm based on the recovery of information in the graph wavelet domain. At each step the damaged structure are estimated by computing the non local graph then we apply the graph wavelet regularization model using the SGWT coefficient. The results are very encouraging and highlight the use of the perceptual informations. In the last strategy, we propose a new approach of decomposition for signals defined on a complete graphs. This method is based on the exploitation of of the laplacian matrix proprieties of the complete graph. In the context of image processing, the use of the color distance is essential to identify the specificities of the color image. This approach opens new perspectives for an in-depth study of its behavior.

Keywords : Color image processing, image denoising, inpainting, multi-scale decomposition on graph, spectral graph wavelet transform.