Multifractal-based texture segmentation using variational procedure

The present contribution aims at segmenting a scale-free texture into different regions, characterized by an a priori (unknown) multifractal spectrum. The multifractal properties are quantified using multiscale quantities C_{1, j} and C_{2, j} that quantify the evolution along the analysis scales 2^j of the empirical mean and variance of a nonlinear transform of wavelet coefficients. The segmentation is performed jointly across all the scales j on the concatenation of both C_{1, j} and C_{2, j} by an efficient vectorial extension of a convex relaxation of the piecewise constant Potts segmentation problem. We provide comparisons with the scalar segmentation of the Hölder exponent as well as independent vectorial segmentations over C₁ and C₂.