Image segmentation with a finite element method

Blaise Bourdin

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    The Mumford-Shah functional for image segmentation is an original approach of the image segmentation problem, based on a minimal energy criterion. Its minimization can be seen as a free discontinuity problem and is based on \Gamma-convergence and bounded variation functions theories.Some new regularization results, make possible to imagine a finite element resolution method.In a first time, the Mumford-Shah functional is introduced and some existing results are quoted. Then, a discrete formulation for the Mumford-Shah problem is proposed and its $\Gamma$-convergence is proved. Finally, some numerical results, computed from both artificial and real images are presented and discussed.
    Original languageEnglish
    JournalModelisation Mathematique et Analyse Numerique
    Issue number2
    Pages (from-to)229-244
    Publication statusPublished - 1999

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