Strongly Convex Optimization for Joint Fractal Feature Estimation and Texture Segmentation

TL;DR

This paper develops and compares strongly convex optimization methods for joint texture segmentation based on fractal features, demonstrating improved accuracy and efficiency in processing large images.

Contribution

It introduces accelerated primal-dual algorithms for convex texture segmentation that jointly analyze local variance and regularity, enhancing segmentation performance.

Findings

Combining local variance and regularity improves segmentation accuracy.

Accelerated algorithms significantly reduce computational costs.

Joint feature analysis outperforms single-feature approaches.

Abstract

The present work investigates the segmentation of textures by formulating it as a strongly convex optimization problem, aiming to favor piecewise constancy of fractal features (local variance and local regularity) widely used to model real-world textures in numerous applications very different in nature. Two objective functions combining these two features are compared, referred to as joint and coupled, promoting either independent or co-localized changes in local variance and regularity. To solve the resulting convex nonsmooth optimization problems, because the processing of large size images and databases are targeted, two categories of proximal algorithms (dual forward-backward and primal-dual), are devised and compared. An in-depth study of the objective functions, notably of their strong convexity, memory and computational costs, permits to propose significantly accelerated algorithms. A class of synthetic models of piecewise fractal texture is constructed and studied. They enable, by means of large-scale Monte-Carlo simulations, to quantify the benefits in texture segmentation of combining local regularity and local variance (as opposed to regularity only) while using strong-convexity accelerated primal-dual algorithms. Achieved results also permit to discuss the gains/costs in imposing co-localizations of changes in local regularity and local variance in the problem formulation. Finally, the potential of the proposed approaches is illustrated on real-world textures taken from a publicly available and documented database.