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. {\textcopyright} 1999 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.

}, isbn = {0031-3203}, author = {Zoltan Kato and Josiane Zerubia and Mark Berthod} } @article {1237, title = {Bayesian image classification using Markov random fields}, journal = {IMAGE AND VISION COMPUTING}, volume = {14}, year = {1996}, note = {UT: A1996UT58100004ScopusID: 0030148684doi: 10.1016/0262-8856(95)01072-6}, month = {1996///}, pages = {285 - 295}, abstract = {In 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).

}, isbn = {0262-8856}, author = {Mark Berthod and Zoltan Kato and Shan Yu and Josiane Zerubia} } @article {1238, title = {A Hierarchical Markov Random Field Model and Multitemperature Annealing for Parallel Image Classification}, journal = {GRAPHICAL MODELS AND IMAGE PROCESSING}, volume = {58}, year = {1996}, note = {UT: A1996TZ03400002ScopusID: 0029732459doi: 10.1006/gmip.1996.0002}, month = {1996///}, pages = {18 - 37}, abstract = {In 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). {\textcopyright} 1996 Academic Press, Inc.

}, isbn = {1077-3169}, author = {Zoltan Kato and Mark Berthod and Josiane Zerubia} } @inbook {1261, title = {Multi-Temperature Annealing: A New Approach for the Energy-Minimization of Hierarchical Markov Random Field Models}, booktitle = {Proceedings of the 12th IAPR International Conference on Pattern Recognition}, year = {1994}, note = {doi: 10.1109/ICPR.1994.576342}, month = {1994///}, pages = {520 - 522}, publisher = {IEEE}, organization = {IEEE}, address = {Los Alamitos}, author = {Josiane Zerubia and Zoltan Kato and Mark Berthod}, editor = {IEEE Computer *Society} } @inbook {1250, title = {Bayesian Image Classification Using Markov Random Fields}, booktitle = {Maximum Entropy and Bayesian Methods}, year = {1993}, month = {1993///}, pages = {375 - 382}, publisher = {Kluwer Academic Publishers}, organization = {Kluwer Academic Publishers}, address = {Dordrecht; Boston; London}, author = {Zoltan Kato and Josiane Zerubia and Mark Berthod}, editor = {Ali Mohammad-Djafari and Guy Demoment} } @booklet {1271, title = {Extraction d{\textquoteright}information dans les images SPOT}, year = {1993}, month = {1993///}, author = {Mark Berthod and Gerard Giraudon and Shan Liu and Frank Mangin and Zoltan Kato and Sabine Urago and Josiane Zerubia} } @booklet {1272, title = {A Hierarchical Markov Random Field Model and Multi-Temperature Annealing for Parallel Image Classification}, year = {1993}, month = {1993///}, url = {http://hal.inria.fr/inria-00074736/}, author = {Zoltan Kato and Mark Berthod and Josiane Zerubia} } @conference {1262, title = {A Hierarchical Markov Random Field Model for Image Classification}, booktitle = {International Workshop on Image and Multidimensional Digital Signal Processing (IMDSP)}, year = {1993}, note = {Art. No.: imdsp.ps}, month = {Sep 1993}, publisher = {IEEE Computer Soc. Pr.}, organization = {IEEE Computer Soc. Pr.}, author = {Zoltan Kato and Mark Berthod and Josiane Zerubia} } @booklet {1273, title = {Image Classification Using Markov Random Fields with Two New Relaxation Methods}, year = {1992}, month = {1992///}, url = {http://hal.inria.fr/docs/00/07/49/54/PDF/RR-1606.pdf}, author = {Zoltan Kato and Josiane Zerubia and Mark Berthod} } @conference {1263, title = {Satellite Image Classification Using a Modified Metropolis Dynamics}, booktitle = {International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, year = {1992}, note = {doi: 10.1109/ICASSP.1992.226148}, month = {Mar 1992}, pages = {573 - 576}, publisher = {IEEE Computer Soc. Pr.}, organization = {IEEE Computer Soc. Pr.}, author = {Zoltan Kato and Josiane Zerubia and Mark Berthod} }