Bayesian Image Classification Using Markov Random Fields

Kato, Zoltan; Zerubia, Josiane; Berthod, Mark

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).}
}