In this thesis, we investigate the different image decomposition models wich permit to separate an image into two components: the structures (or objects) and the textures. This work is based on the model proposed by Yves Meyer in 1999 and the recent work on the algorithms of Jean-François Aujol.After a theoretic study of these models, we propose to extend the model to the case of noisy images in order to get a decomposition into three components: structures + textures + noise.Moreover, we propose an evaluation method in order to be able to compare the results given by each algorithm.In the last part of this thesis, we show different application of these decomposition methods. Specially, we propose an algorithm to detect the roads network in aerial images. This algorithm combines image decomposition, Gestalt's alignment detection algorithm and active contours.
