Nonsmooth Convex Joint Estimation of Local Regularity and Local Variance for Fractal Texture Segmentation
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Fractal models are widely used to describe realworld textures in numerous real-world applications very different in nature. The present work investigates estimation/segmentation of piecewise fractal textures by framing the problem into several alternative convex optimization formulations, aiming to favor piecewise constancy of local regularity and local variance, the two parameters that characterize fractal textures. Two categories of proximal algorithms (dual forward-backward and primaldual), used to solve convex nonsmooth optimization problems, are devised and compared. An in-depth study of the objective functions, notably strong convexity, permits to propose significantly accelerated algorithms. A synthetic model of piecewise fractal texture is constructed and studied. It enables, by means of Monte Carlo simulations, to quantity the benefits in texture segmentation of using together local regularity and local variance (as opposed to the regularity only) as well as of using stongconvexity accelerated primal-dual algorithms. Achieved results also permit to discuss the gains/costs in imposing or not in the problem formulation co-localizations of changes in local regularity and local variance.
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