by Zoltan Kato, Josiane Zerubia, Mark Berthod
Abstract:
In this paper, we present two relaxation techniques: Deterministic Pseudo-Annealing (DPA) and Modified Metropolis Dynamics (MMD) in order to do image classification using a Markov Random Field modelization. For the first algorithm (DPA), the a posteriori probability of a tentative labeling is generalized to continuous labeling. The merit function thus defined has the same maxima under constraints yielding probability vectors. Changing these constraints convexify the merit function. The algorithm solve this unambigous maximization problem and then tracks down the solution while the original constraints are restored yielding a good even if suboptimal solution to the original labeling assignment problem. As for the second method (MMD), it is a modified version of the Metropolis algorithm: at each iteration the new state is chosen randomly but the decision to accept it is purely deterministic. This is of course also a suboptimal technique which gives faster results than stochastic relaxation. These two methods have been implemented on a Connection Machine CM2 and simulation results are shown with a SPOT image and two synthetic noisy images. These results are compared to those obtained with the Metropolis algorithm, the Gibbs sampler and ICM (Iterated Conditional Mode).
Reference:
Zoltan Kato, Josiane Zerubia, Mark Berthod, Bayesian Image Classification Using Markov Random Fields, Chapter in Maximum Entropy and Bayesian Methods (Ali Mohammad-Djafari, Guy Demoment, eds.), pp. 375-382, 1993, Kluwer Academic Publisher.
Bibtex Entry:
@string{kluwer="Kluwer Academic Publisher"}
@InCollection{Kato-etal93,
author = {Kato, Zoltan and Zerubia, Josiane and Berthod, Mark},
title = {{B}ayesian Image Classification Using {M}arkov
Random Fields},
booktitle = {Maximum Entropy and {B}ayesian Methods},
pages = {375--382},
year = 1993,
editor = {Mohammad-Djafari, Ali and Demoment, Guy},
publisher = kluwer,
abstract = {In this paper, we present two relaxation techniques:
Deterministic Pseudo-Annealing (DPA) and Modified
Metropolis Dynamics (MMD) in order to do image
classification using a Markov Random Field
modelization. For the first algorithm (DPA), the a
posteriori probability of a tentative labeling is
generalized to continuous labeling. The merit
function thus defined has the same maxima under
constraints yielding probability vectors. Changing
these constraints convexify the merit function. The
algorithm solve this unambigous maximization problem
and then tracks down the solution while the original
constraints are restored yielding a good even if
suboptimal solution to the original labeling
assignment problem. As for the second method (MMD),
it is a modified version of the Metropolis
algorithm: at each iteration the new state is chosen
randomly but the decision to accept it is purely
deterministic. This is of course also a suboptimal
technique which gives faster results than stochastic
relaxation. These two methods have been implemented
on a Connection Machine CM2 and simulation results
are shown with a SPOT image and two synthetic noisy
images. These results are compared to those obtained
with the Metropolis algorithm, the Gibbs sampler and
ICM (Iterated Conditional Mode).}
}