Multivariate optimization for multifractal-based texture segmentation

This work aims to segment a texture into different regions, each characterized by a priori unknown multifractal properties. The multifractal properties are quantified using the multiscale function C_1,j that quantifies the evolution along analysis scales 2^j of the empirical mean of the log of the wavelet leaders. The segmentation procedure is applied to local estimate of C_1,j. It involves a multivariate Mumford-Shah relaxation formulated as a convex optimization problem involving a structure tensor penalization and an efficient algorithmic solution based on primal-dual proximal algorithm. The performances are evaluated on synthetic textures.