Local regularity for texture segmentation: Combining wavelet leaders and proximal minimization

Texture segmentation constitutes a classical yet crucial task in image processing. In many applications of very different natures (biomedical, geophysics,...) textures are naturally defined in terms of their local regularity fluctuations, which can be quantified as the variations of local Hölder exponents. Furthermore, such images are often naturally embedded in the class of piece-wise constant local regularity functions. The present contribution aims at proposing and assessing a segmentation procedure for this class of images. Its originality is twofold: First, local regularity is estimated using wavelet leaders, a novel multiresolution quantity recently introduced for multifractal analysis but barely used in local regularity measurement, comparisons against wavelet coefficient based estimation are conducted; Second, the challenging minimal partition problem underlying segmentation is convexified and conducted within a customized proximal framework. The estimation of the number of regions and their target regularity is obtained from a total-variation estimate that enables the actual use of proximal minimization for texture segmentation. Performance is assessed and illustrated on synthetic textures.