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Image segmentation with a finiteelement method

Published online by Cambridge University Press:  15 August 2002

Blaise Bourdin
Blaise Bourdin*
Affiliation:
LPMTM, Institut Galilée, Université Paris Nord, avenue J.B. Clément, 93430 Villetaneuse, France. Department of Mathematics, Technical University of Denmark, 2800 Lyngby, Denmark. bourdin@mat.dtu.dk.
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Abstract

The Mumford-Shah functional for image segmentation is an original approachof the image segmentation problem, based on a minimal energy criterion. Itsminimization can be seen as a free discontinuity problem and is based onΓ-convergence and bounded variation functions theories. Some newregularization results, make possible to imagine a finite element resolutionmethod. In a first time, the Mumford-Shah functional isintroduced and some existing results are quoted. Then, adiscrete formulation for the Mumford-Shah problem is proposedand its Γ-convergence is proved. Finally, somenumerical results, computed from both artificial and realimages are presented and discussed.

Keywords

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 2 , March 1999 , pp. 229 - 244
Copyright
© EDP Sciences, SMAI, 1999

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