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Exact Optimization of Discrete Constrained Total Variation Minimization Problems

  • Jérôme Darbon
  • Marc Sigelle
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3322)

Abstract

This paper deals with the total variation minimization problem when the fidelity is either the L 2-norm or the L 1-norm. We propose an algorithm which computes the exact solution of these two problems after discretization. Our method relies on the decomposition of an image into its level sets. It maps the original problems into independent binary Markov Random Field optimization problems associated with each level set. Exact solutions of these binary problems are found thanks to minimum-cut techniques. We prove that these binary solutions are increasing and thus allow to reconstruct the solution of the original problems.

Keywords

Monotone Property Markov Random Field Level Line Gradient Descent Algorithm Binary Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Jérôme Darbon
    • 1
    • 2
  • Marc Sigelle
    • 2
  1. 1.EPITA Research and Development Laboratory (LRDE)Le Kremlin-BicêtreFrance
  2. 2.ENST TSI / CNRS LTCI UMR 5141ParisFrance

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