This paper deals with the problem of unsupervised classification of images modeled by Markov random fields (MRF). If the model parameters are known then we have various methods to solve the segmentation problem (simulated annealing (SA), iterated conditional modes (ICM), etc). However, when the parameters are unknown, the problem becomes more difficult. One has to estimate the hidden label field parameters only from the observed image. Herein, we are interested in parameter estimation methods related to monogrid and hierarchical MRF models. The basic idea is similar to the expectation-maximization (EM) algorithm: we recursively look at the maximum a posteriori (MAP) estimate of the label field given the estimated parameters, then we look at the maximum likelihood (ML) estimate of the parameters given a tentative labeling obtained at the previous step. The only parameter supposed to be known is the number of classes, all the other parameters are estimated. The proposed algorithms have been implemented on a Connection Machine CM200. Comparative experiments have been performed on both noisy synthetic data and real images. © 1999 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.

%B PATTERN RECOGNITION %V 32 %P 591 - 604 %8 1999/// %@ 0031-3203 %G eng %N 4 %! PATTERN RECOGN %0 Journal Article %J IMAGE AND VISION COMPUTING %D 1996 %T Bayesian image classification using Markov random fields %A Mark Berthod %A Zoltan Kato %A Shan Yu %A Josiane Zerubia %XIn this paper, we present three optimisation techniques, Deterministic Pseudo-Annealing (DPA), Game Strategy Approach (GSA), and Modified Metropolis Dynamics (MMD), in order to carry out image classification using a Markov random field model. For the first approach (DPA), the a posteriori probability of a tentative labelling is generalised to a continuous labelling. The merit function thus defined has the same maxima under constraints yielding probability vectors. Changing these constraints convexifies the merit function. The algorithm solves this unambiguous maximisation problem, and then tracks down the solution while the original constraints are restored yielding a good, even if suboptimal, solution to the original labelling assignment problem. In the second method (GSA), the maximisation problem of the a posteriori probability of the labelling is solved by an optimisation algorithm based on game theory. A non-cooperative n-person game with pure strategies is designed such that the set of Nash equilibrium points of the game is identical to the set of local maxima of the a posteriori probability of the labelling. The algorithm converges to a Nash equilibrium. The third method (MMD) 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 also a suboptimal technique but it is much faster than stochastic relaxation. These three methods have been implemented on a Connection Machine CM2. Experimental results are compared to those obtained by the Metropolis algorithm, the Gibbs sampler and ICM (Iterated Conditional Mode).

%B IMAGE AND VISION COMPUTING %V 14 %P 285 - 295 %8 1996/// %@ 0262-8856 %G eng %N 4 %! IMAGE VISION COMPUT %0 Journal Article %J GRAPHICAL MODELS AND IMAGE PROCESSING %D 1996 %T A Hierarchical Markov Random Field Model and Multitemperature Annealing for Parallel Image Classification %A Zoltan Kato %A Mark Berthod %A Josiane Zerubia %XIn this paper, we are interested in massively parallel multiscale relaxation algorithms applied to image classification. It is well known that multigrid methods can improve significantly the convergence rate and the quality of the final results of iterative relaxation techniques. First, we present a classical multiscale model which consists of a label pyramid and a whole observation field. The potential functions of coarser grids are derived by simple computations. The optimization problem is first solved at the higher scale by a parallel relaxation algorithm; then the next lower scale is initialized by a projection of the result. Second, we propose a hierarchical Markov random field model based on this classical model. We introduce new interactions between neighbor levels in the pyramid. It can also be seen as a way to incorporate cliques with far apart sites for a reasonable price. This model results in a relaxation algorithm with a new annealing scheme: the multitemperature annealing (MTA) scheme, which consists of associating higher temperatures to higher levels, in order to be less sensitive to local minima at coarser grids. The convergence to the global optimum is proved by a generalization of the annealing theorem of S. Geman and D. Geman (IEEE Trans. Pattern Anal. Mach. Intell. 6, 1984, 721-741). © 1996 Academic Press, Inc.

%B GRAPHICAL MODELS AND IMAGE PROCESSING %V 58 %P 18 - 37 %8 1996/// %@ 1077-3169 %G eng %N 1 %! GRAPH MODEL IM PROC %0 Book Section %B Proceedings of the 12th IAPR International Conference on Pattern Recognition %D 1994 %T Multi-Temperature Annealing: A New Approach for the Energy-Minimization of Hierarchical Markov Random Field Models %A Josiane Zerubia %A Zoltan Kato %A Mark Berthod %E IEEE Computer *Society %B Proceedings of the 12th IAPR International Conference on Pattern Recognition %I IEEE %C Los Alamitos %P 520 - 522 %8 1994/// %G eng %0 Book Section %B Maximum Entropy and Bayesian Methods %D 1993 %T Bayesian Image Classification Using Markov Random Fields %A Zoltan Kato %A Josiane Zerubia %A Mark Berthod %E Ali Mohammad-Djafari %E Guy Demoment %B Maximum Entropy and Bayesian Methods %I Kluwer Academic Publishers %C Dordrecht; Boston; London %P 375 - 382 %8 1993/// %G eng %0 Generic %D 1993 %T Extraction d'information dans les images SPOT %A Mark Berthod %A Gerard Giraudon %A Shan Liu %A Frank Mangin %A Zoltan Kato %A Sabine Urago %A Josiane Zerubia %8 1993/// %G eng %0 Generic %D 1993 %T A Hierarchical Markov Random Field Model and Multi-Temperature Annealing for Parallel Image Classification %A Zoltan Kato %A Mark Berthod %A Josiane Zerubia %8 1993/// %G eng %U http://hal.inria.fr/inria-00074736/ %0 Conference Paper %B International Workshop on Image and Multidimensional Digital Signal Processing (IMDSP) %D 1993 %T A Hierarchical Markov Random Field Model for Image Classification %A Zoltan Kato %A Mark Berthod %A Josiane Zerubia %B International Workshop on Image and Multidimensional Digital Signal Processing (IMDSP) %I IEEE Computer Soc. Pr. %8 Sep 1993 %G eng %0 Generic %D 1992 %T Image Classification Using Markov Random Fields with Two New Relaxation Methods %A Zoltan Kato %A Josiane Zerubia %A Mark Berthod %8 1992/// %G eng %U http://hal.inria.fr/docs/00/07/49/54/PDF/RR-1606.pdf %0 Conference Paper %B International Conference on Acoustics, Speech and Signal Processing (ICASSP) %D 1992 %T Satellite Image Classification Using a Modified Metropolis Dynamics %A Zoltan Kato %A Josiane Zerubia %A Mark Berthod %B International Conference on Acoustics, Speech and Signal Processing (ICASSP) %I IEEE Computer Soc. Pr. %P 573 - 576 %8 Mar 1992 %G eng