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 C1 and C2 that quantify the evolution along the analysis scale of the empirical mean and variance of a nonlinear transform of wavelet coefficients. The segmentation is performed jointly across all the scales on the concatenation of both C1 and C2 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 Holder exponent as well as independent vectorial segmentations over C1 and C2.