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.

1 aKato, Zoltan1 aZerubia, Josiane1 aBerthod, Mark uhttps://www.inf.u-szeged.hu/publication/unsupervised-parallel-image-classification-using-markovian-models02227nas a2200181 4500008004100000020001400041245006100055210006100116260001200177300001400189490000700203520166500210100001801875700001701893700001301910700002101923856010101944 1996 eng d a0262-885600aBayesian image classification using Markov random fields0 aBayesian image classification using Markov random fields c1996/// a285 - 2950 v143 aIn 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).

1 aBerthod, Mark1 aKato, Zoltan1 aYu, Shan1 aZerubia, Josiane uhttps://www.inf.u-szeged.hu/publication/bayesian-image-classification-using-markov-random-fields02007nas a2200169 4500008004100000020001400041245011000055210006900165260001200234300001200246490000700258520136600265100001701631700001801648700002101666856015001687 1996 eng d a1077-316900aA Hierarchical Markov Random Field Model and Multitemperature Annealing for Parallel Image Classification0 aHierarchical Markov Random Field Model and Multitemperature Anne c1996/// a18 - 370 v583 aIn 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.

1 aKato, Zoltan1 aBerthod, Mark1 aZerubia, Josiane uhttps://www.inf.u-szeged.hu/publication/a-hierarchical-markov-random-field-model-and-multitemperature-annealing-for-parallel-image-classification00664nas a2200145 4500008004100000245011900041210006900160260003200229300001400261100002100275700001700296700001800313700002900331856015800360 1994 eng d00aMulti-Temperature Annealing: A New Approach for the Energy-Minimization of Hierarchical Markov Random Field Models0 aMultiTemperature Annealing A New Approach for the EnergyMinimiza aLos AlamitosbIEEEc1994/// a520 - 5221 aZerubia, Josiane1 aKato, Zoltan1 aBerthod, Mark1 a*Society, IEEE, Computer uhttps://www.inf.u-szeged.hu/publication/multi-temperature-annealing-a-new-approach-for-the-energy-minimization-of-hierarchical-markov-random-field-models00605nas a2200157 4500008004100000245006100041210006100102260006700163300001400230100001700244700002100261700001800282700002600300700001800326856010300344 1993 eng d00aBayesian Image Classification Using Markov Random Fields0 aBayesian Image Classification Using Markov Random Fields aDordrecht; Boston; LondonbKluwer Academic Publishersc1993/// a375 - 3821 aKato, Zoltan1 aZerubia, Josiane1 aBerthod, Mark1 aMohammad-Djafari, Ali1 aDemoment, Guy uhttps://www.inf.u-szeged.hu/publication/bayesian-image-classification-using-markov-random-fields-000538nas a2200169 4500008004100000245005000041210004900091260001200140100001800152700002100170700001400191700001800205700001700223700001800240700002100258856008900279 1993 eng d00aExtraction d'information dans les images SPOT0 aExtraction dinformation dans les images SPOT c1993///1 aBerthod, Mark1 aGiraudon, Gerard1 aLiu, Shan1 aMangin, Frank1 aKato, Zoltan1 aUrago, Sabine1 aZerubia, Josiane uhttps://www.inf.u-szeged.hu/publication/extraction-dinformation-dans-les-images-spot00451nas a2200121 4500008004100000245011100041210006900152260001200221100001700233700001800250700002100268856004000289 1993 eng d00aA Hierarchical Markov Random Field Model and Multi-Temperature Annealing for Parallel Image Classification0 aHierarchical Markov Random Field Model and MultiTemperature Anne c1993///1 aKato, Zoltan1 aBerthod, Mark1 aZerubia, Josiane uhttp://hal.inria.fr/inria-00074736/00504nas a2200121 4500008004100000245007000041210006800111260003700179100001700216700001800233700002100251856011000272 1993 eng d00aA Hierarchical Markov Random Field Model for Image Classification0 aHierarchical Markov Random Field Model for Image Classification bIEEE Computer Soc. Pr.cSep 19931 aKato, Zoltan1 aBerthod, Mark1 aZerubia, Josiane uhttps://www.inf.u-szeged.hu/publication/a-hierarchical-markov-random-field-model-for-image-classification00441nas a2200121 4500008004100000245008400041210006900125260001200194100001700206700002100223700001800244856005700262 1992 eng d00aImage Classification Using Markov Random Fields with Two New Relaxation Methods0 aImage Classification Using Markov Random Fields with Two New Rel c1992///1 aKato, Zoltan1 aZerubia, Josiane1 aBerthod, Mark uhttp://hal.inria.fr/docs/00/07/49/54/PDF/RR-1606.pdf00535nas a2200133 4500008004100000245007200041210006900113260003700182300001400219100001700233700002100250700001800271856011200289 1992 eng d00aSatellite Image Classification Using a Modified Metropolis Dynamics0 aSatellite Image Classification Using a Modified Metropolis Dynam bIEEE Computer Soc. Pr.cMar 1992 a573 - 5761 aKato, Zoltan1 aZerubia, Josiane1 aBerthod, Mark uhttps://www.inf.u-szeged.hu/publication/satellite-image-classification-using-a-modified-metropolis-dynamics