Approximation of maximal Cheeger sets by projection

Guillaume Carlier; Myriam Comte; Gabriel Peyré

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2009)

  • Volume: 43, Issue: 1, page 139-150
  • ISSN: 0764-583X

Abstract

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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 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.

How to cite

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Carlier, Guillaume, Comte, Myriam, and Peyré, Gabriel. "Approximation of maximal Cheeger sets by projection." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 43.1 (2009): 139-150. <http://eudml.org/doc/245646>.

@article{Carlier2009,
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.},
author = {Carlier, Guillaume, Comte, Myriam, Peyré, Gabriel},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Cheeger sets; Cheeger constant; total variation minimization; projections; Cheeger set; Cheeger constants; landslide modeling; continuous maximal flow problem},
language = {eng},
number = {1},
pages = {139-150},
publisher = {EDP-Sciences},
title = {Approximation of maximal Cheeger sets by projection},
url = {http://eudml.org/doc/245646},
volume = {43},
year = {2009},
}

TY - JOUR
AU - Carlier, Guillaume
AU - Comte, Myriam
AU - Peyré, Gabriel
TI - Approximation of maximal Cheeger sets by projection
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2009
PB - EDP-Sciences
VL - 43
IS - 1
SP - 139
EP - 150
AB - 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.
LA - eng
KW - Cheeger sets; Cheeger constant; total variation minimization; projections; Cheeger set; Cheeger constants; landslide modeling; continuous maximal flow problem
UR - http://eudml.org/doc/245646
ER -

References

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