Rate of convergence of the Swendsen-Wang dynamics in image segmentation problems: a theoretical and experimental study

Isabelle Gaudron

ESAIM: Probability and Statistics (2010)

  • Volume: 1, page 259-284
  • ISSN: 1292-8100

Abstract

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We study in this paper the convergence rate of the Swendsen-Wang dynamics towards its equilibrium law, when the energy belongs to a large family of energies used in image segmentation problems. We compute the exponential equivalents of the transitions which control the process at low temperature, as well as the critical constant which gives its convergence rate. We give some theoretical tools to compare this dynamics with Metropolis, and develop an experimental study in order to calibrate both dynamics performances in image segmentation problems.

How to cite

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Gaudron, Isabelle. "Rate of convergence of the Swendsen-Wang dynamics in image segmentation problems: a theoretical and experimental study." ESAIM: Probability and Statistics 1 (2010): 259-284. <http://eudml.org/doc/197778>.

@article{Gaudron2010,
abstract = { We study in this paper the convergence rate of the Swendsen-Wang dynamics towards its equilibrium law, when the energy belongs to a large family of energies used in image segmentation problems. We compute the exponential equivalents of the transitions which control the process at low temperature, as well as the critical constant which gives its convergence rate. We give some theoretical tools to compare this dynamics with Metropolis, and develop an experimental study in order to calibrate both dynamics performances in image segmentation problems. },
author = {Gaudron, Isabelle},
journal = {ESAIM: Probability and Statistics},
keywords = {Stochastic dynamics / Metropolis dynamics / Swendsen-Wang dynamics / image segmentation / Markov processes.; Metropolis relaxation; Swendsen-Wang dynamics; image segmentation problems},
language = {eng},
month = {3},
pages = {259-284},
publisher = {EDP Sciences},
title = {Rate of convergence of the Swendsen-Wang dynamics in image segmentation problems: a theoretical and experimental study},
url = {http://eudml.org/doc/197778},
volume = {1},
year = {2010},
}

TY - JOUR
AU - Gaudron, Isabelle
TI - Rate of convergence of the Swendsen-Wang dynamics in image segmentation problems: a theoretical and experimental study
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 1
SP - 259
EP - 284
AB - We study in this paper the convergence rate of the Swendsen-Wang dynamics towards its equilibrium law, when the energy belongs to a large family of energies used in image segmentation problems. We compute the exponential equivalents of the transitions which control the process at low temperature, as well as the critical constant which gives its convergence rate. We give some theoretical tools to compare this dynamics with Metropolis, and develop an experimental study in order to calibrate both dynamics performances in image segmentation problems.
LA - eng
KW - Stochastic dynamics / Metropolis dynamics / Swendsen-Wang dynamics / image segmentation / Markov processes.; Metropolis relaxation; Swendsen-Wang dynamics; image segmentation problems
UR - http://eudml.org/doc/197778
ER -

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