Approximation of maximal Cheeger sets by projection

Guillaume Carlier; Myriam Comte; Gabriel Peyré

ESAIM: Mathematical Modelling and Numerical Analysis (2008)

  • 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 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 43.1 (2008): 139-150. <http://eudml.org/doc/194441>.

@article{Carlier2008,
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},
keywords = {Cheeger sets; Cheeger constant; total variation minimization; projections.; Cheeger set; Cheeger constants; projections; landslide modeling; continuous maximal flow problem},
language = {eng},
month = {10},
number = {1},
pages = {139-150},
publisher = {EDP Sciences},
title = {Approximation of maximal Cheeger sets by projection},
url = {http://eudml.org/doc/194441},
volume = {43},
year = {2008},
}

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
DA - 2008/10//
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; projections; landslide modeling; continuous maximal flow problem
UR - http://eudml.org/doc/194441
ER -

References

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