Segmentation of anisotropic scale-free textures based on dual-tree wavelet analysis and proximal optimization

Texture segmentation is a key task in image processing for which many models have been considered. In this work we focus on textures characterized by anisotropy and scale-free statistics, two generic properties of use to model numerous real-world applications. In a first part, we will describe how wavelet analysis permits to extract those statistical properties. Based on these results, we propose to combine a complex dual-tree multiscale (wavelet) analysis within an inverse problem formulation in order to estimate anisotropic scale-free local parameters and to group them into piecewise homogeneous patches, jointly and in one single step. In a second part, we provide an algorithmic solution to minimize the corresponding functional. A primal-dual proximal convergent algorithm is devised and accelerated by taking advantage of the strong convexity of the data-fidelity term. The third part is dedicated to the automatic estimation of the regularization parameter without requiring knowledge of the ground truth using Stein's Unbiased Risk Estimate.