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

Published online by Cambridge University Press:  15 August 2002

Isabelle Gaudron
Isabelle Gaudron*
Affiliation:
gaudron@cmla.ens-cachan.fr
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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.

Keywords

Stochastic dynamics / Metropolis dynamics / Swendsen-Wang dynamics / image segmentation / Markov processes.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 1 , 1997 , pp. 259 - 284
Copyright
© EDP Sciences, SMAI, 1997

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