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<sub>1, j</sub> and C<sub>2, j</sub> that quantify the evolution along the analysis scales 2<sup>j</sup> 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<sub>1, j</sub> and C<sub>2, j</sub> 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 C<sub>1</sub> and C<sub>2</sub>.