Multifractal-based texture segmentation using variational procedure

J. Frecon, N. Pustelnik, H. Wendt, L. Condat and P. Abry
Image, Video, and Multidimensional Signal Processing Workshop (IVMSP), 2016


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.


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