Journal of Mathematical Imaging and Vision

, Volume 26, Issue 3, pp 277–291 | Cite as

Image Restoration with Discrete Constrained Total Variation Part II: Levelable Functions, Convex Priors and Non-Convex Cases

  • Jérôme Darbon
  • Marc Sigelle


In Part II of this paper we extend the results obtained in Part I for total variation minimization in image restoration towards the following directions: first we investigate the decomposability property of energies on levels, which leads us to introduce the concept of levelable regularization functions (which TV is the paradigm of). We show that convex levelable posterior energies can be minimized exactly using the level-independant cut optimization scheme seen in Part I. Next we extend this graph cut scheme to the case of non-convex levelable energies.We present convincing restoration results for images corrupted with impulsive noise. We also provide a minimum-cost based algorithm which computes a global minimizer for Markov Random Field with convex priors. Last we show that non-levelable models with convex local conditional posterior energies such as the class of generalized Gaussian models can be exactly minimized with a generalized coupled Simulated Annealing.


total variation level sets convexity Markov Random fields graph cuts levelable functions 



Kluwer Academic Publishers


Electronically submitted article


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© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.EPITA Research and Development Laboratory (LRDE)Le Kremlin-BicêtreFrance
  2. 2.École Nationale Supérieure des Télécommunications (ENST)ParisFrance
  3. 3.École Nationale Supérieure des Télécommunications (ENST) / LTCI CNRS UMR 5141ParisFrance

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