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International Journal of Computer Vision

, Volume 67, Issue 1, pp 111–136 | Cite as

Structure-Texture Image Decomposition—Modeling, Algorithms, and Parameter Selection

  • Jean-François AujolEmail author
  • Guy Gilboa
  • Tony Chan
  • Stanley Osher
Article

Abstract

This paper explores various aspects of the image decomposition problem using modern variational techniques. We aim at splitting an original image f into two components u and ρ, where u holds the geometrical information and ρ holds the textural information. The focus of this paper is to study different energy terms and functional spaces that suit various types of textures. Our modeling uses the total-variation energy for extracting the structural part and one of four of the following norms for the textural part: L2, G, L1 and a new tunable norm, suggested here for the first time, based on Gabor functions. Apart from the broad perspective and our suggestions when each model should be used, the paper contains three specific novelties: first we show that the correlation graph between u and ρ may serve as an efficient tool to select the splitting parameter, second we propose a new fast algorithm to solve the TVL1 minimization problem, and third we introduce the theory and design tools for the TV-Gabor model.

Keywords

image decomposition restoration parameter selection BV G L1 Hilbert space projection total-variation Gabor functions 

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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  • Jean-François Aujol
    • 1
    • 2
    Email author
  • Guy Gilboa
    • 1
  • Tony Chan
    • 1
  • Stanley Osher
    • 1
  1. 1.Department of MathematicsUCLALos AngelesUSA
  2. 2.CMLA (CNRS UMR 8536)ENS CachanFrance

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