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 C1,j that quantifies the evolution along analysis scales 2j of the empirical mean of the log of the wavelet leaders. The segmentation procedure is applied to local estimate of C1,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.