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Approximation of maximal Cheeger sets by projection

Published online by Cambridge University Press:  16 October 2008

Guillaume Carlier ,
Myriam Comte  and
Gabriel Peyré
Guillaume Carlier
Affiliation:
CEREMADE, Université Paris Dauphine, France. carlier@ceremade.dauphine.fr; peyre@ceremade.dauphine.fr
Myriam Comte
Affiliation:
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, France. comte@ann.jussieu.fr
Gabriel Peyré
Affiliation:
CEREMADE, Université Paris Dauphine, France. carlier@ceremade.dauphine.fr; peyre@ceremade.dauphine.fr
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Abstract

This article deals with the numerical computation of the Cheeger constant and the approximation of the maximal Cheeger set of a given subset of ${\mathbb R}^d$. This problem is motivated by landslide modelling as well as by the continuous maximal flow problem. Using the fact that the maximal Cheeger set can be approximated by solving a rather simple projection problem, we propose a numerical strategy to compute maximal Cheeger sets and Cheeger constants.

Keywords

Cheeger setsCheeger constanttotal variation minimizationprojections.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 43 , Issue 1 , January 2009 , pp. 139 - 150
Copyright
© EDP Sciences, SMAI, 2008

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