Combining Dual-Tree Wavelet Analysis and Proximal Optimization for Anisotropic Scale-Free Texture Segmentation

The present work addresses the segmentation of textures characterized by anisotropy and scale-free statistics, two generic properties of use to model numerous real-world applications. This is achieved by proposing to combine a complex dual-tree multi-scale (wavelet) analysis within an inverse problem formulation aiming to estimate anisotropy and scale-free local parameters and to group them into piecewise homogeneous patches, jointly and in one single step. 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. Segmentation performance are assessed as function of the complexity of the task by means of Monte Carlo simulations conducted over synthetic textures, defined from anisotropic scale-free stochastic models.