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Implementation of an adaptive finite-element approximation of the Mumford-Shah functional

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Summary. We present and detail a method for the numerical solving of the Mumford-Shah problem, based on a finite element method and on adaptive meshes. We start with the formulation introduced in [13], detail its numerical implementation and then propose a variant which is proved to converge to the Mumford-Shah problem. A few experiments are illustrated.

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Authors and Affiliations

  1. LPMTM (CNRS UPR 9001), Institut Galilée, Université Paris Nord, Av. J.-B. Clément, F-93430 Villetaneuse, France; e-mail: Blaise.Bourdin@lpmtm.univ-paris13.fr , , , , , , FR

    Blaise Bourdin

  2. CEREMADE (CNRS UMR 7534), Université de Paris-Dauphine, F-75775 Paris CEDEX 16, France; e-mail: Antonin.Chambolle@ceremade.dauphine.fr , , , , , , FR

    Antonin Chambolle

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  1. Blaise Bourdin
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  2. Antonin Chambolle
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Received October 8, 1998 / Published online: April 20, 2000

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Bourdin, B., Chambolle, A. Implementation of an adaptive finite-element approximation of the Mumford-Shah functional. Numer. Math. 85, 609–646 (2000). https://doi.org/10.1007/PL00005394

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  • DOI: https://doi.org/10.1007/PL00005394

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