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A Fast and Exact Algorithm for Total Variation Minimization

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Pattern Recognition and Image Analysis (IbPRIA 2005)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3522))

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Abstract

This paper deals with the minimization of the total variation under a convex data fidelity term. We propose an algorithm which computes an exact minimizer of this problem. The method relies on the decomposition of an image into its level sets. Using these level sets, we map the problem into optimizations of independent binary Markov Random Fields. Binary solutions are found thanks to graph-cut techniques and we show how to derive a fast algorithm. We also study the special case when the fidelity term is the L 1-norm. Finally we provide some experiments.

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Author information

Authors and Affiliations

  1. EPITA Research and Development Laboratory (LRDE), 14-16 rue Voltaire, F-94276, Le Kremlin-Bicêtre, France

    Jérôme Darbon

  2. ENST / LTCI CNRS UMR 5141, 46 rue Barrault, F-75013, Paris, France

    Jérôme Darbon & Marc Sigelle

Authors
  1. Jérôme Darbon
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  2. Marc Sigelle
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Editor information

Editors and Affiliations

  1. Instituto Superior Técnico & Instituto de Sistemas e Robótica, 1049-001, Lisboa, Portugal

    Jorge S. Marques

  2. ETSI Informática y e Telecomunicación, University of Granada, 18071, Granada, Spain

    Nicolás Pérez de la Blanca

  3. CERENA-Centro de Recursos Naturais e Ambiente, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001, Lisboa, Portugal

    Pedro Pina

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© 2005 Springer-Verlag Berlin Heidelberg

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Darbon, J., Sigelle, M. (2005). A Fast and Exact Algorithm for Total Variation Minimization. In: Marques, J.S., Pérez de la Blanca, N., Pina, P. (eds) Pattern Recognition and Image Analysis. IbPRIA 2005. Lecture Notes in Computer Science, vol 3522. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11492429_43

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  • DOI: https://doi.org/10.1007/11492429_43

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26153-7

  • Online ISBN: 978-3-540-32237-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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