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total variation minimization

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Approximation of maximal Cheeger sets by projection
Guillaume Carlier, Myriam Comte, Gabriel Peyré
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 43 / Issue 1 / January 2009

Published online by Cambridge University Press:

16 October 2008, pp. 139-150

Print publication:

January 2009
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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.