Multiscale texture separation

TL;DR

This paper introduces a new multiscale texture separation algorithm based on Meyer's image decomposition and Littlewood-Paley filters, capable of nearly perfect texture extraction and extended to directional multiscale separation, validated on synthetic and real images.

Contribution

It presents a novel theorem linking Meyer's model with Littlewood-Paley filters for effective texture separation and introduces a parameterless, multiscale, and directional algorithm.

Findings

Effective texture separation on synthetic images

Successful application to real images

Enhanced directional multiscale separation

Abstract

In this paper, we investigate theoretically the behavior of Meyer's image cartoon + texture decomposition model. Our main results is a new theorem which shows that, by combining the decomposition model and a well chosen Littlewood-Paley filter, it is possible to extract almost perfectly a certain class of textures. This theorem leads us to the construction of a parameterless multiscale texture separation algorithm. Finally, we propose to extend this algorithm into a directional multiscale texture separation algorithm by designing a directional Littlewood-Paley filter bank. Several experiments show the efficiency of the proposed method both on synthetic and real images.