Journal of Mathematical Imaging and Vision

, Volume 37, Issue 3, pp 232–248 | Cite as

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

  • Vincent Duval
  • Jean-François Aujol
  • Luminita A. Vese
Open Access


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.


Texture modeling Color image decomposition Projected gradient algorithm Color texture modeling 


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Copyright information

© The Author(s) 2010

Authors and Affiliations

  • Vincent Duval
    • 1
  • Jean-François Aujol
    • 2
    • 3
  • Luminita A. Vese
    • 4
  1. 1.Institut TelecomTelecom ParisTech, CNRS UMR 5141Paris cedex 13France
  2. 2.CMLA, ENS CachanCNRS, UniverSudCachanFrance
  3. 3.LATP, CMIUMR CNRS 6632, Université de ProvenceMarseille cedex 13France
  4. 4.UCLA, Mathematics DepartmentLos AngelesUSA

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