Mathematical Modeling of Textures: Application to Color Image Decomposition with a Projected Gradient Algorithm

Authors:
Vincent Duval;Jean-François Aujol;Luminita A. Vese
Affiliations:
Institut Telecom, Telecom ParisTech, CNRS UMR 5141, Paris cedex 13, France 75634;CMLA, ENS Cachan, CNRS, UniverSud, Cachan, France 94230 and LATP, CMI, UMR CNRS 6632, Université de Provence, Marseille cedex 13, France 13453;UCLA, Mathematics Department, Los Angeles, USA 90095-1555
Venue:
Journal of Mathematical Imaging and Vision
Year:
2010

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Abstract

In this paper, we are interested in texture modeling with functional analysis spaces. We focus on the case of color image processing, and in particular color image decomposition. The problem of image decomposition consists in splitting an original image f into two components u and v. u should contain the geometric information of the original image, while v should be made of the oscillating patterns of f, such as textures. We propose here a scheme based on a projected gradient algorithm to compute the solution of various decomposition models for color images or vector-valued images. We provide a direct convergence proof of the scheme, and we give some analysis on color texture modeling.