Random Fields And Spatial Renewal Potentials
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By using an approach similar to that used for Markov random fields, we propose a spatial version of renewal processes, generalizing the usual notion in dimension 1. We characterize the potentials of such renewal random fields and we give a theorem about the presence of phase transition. Finally, we study the problem of the sampling of renewal fields by means of a random automaton, we show simulations and discuss the stopping rules of the process of sampling.
KeywordsRandom Field Cellular Automaton Gibbs Measure Markov Random Field Death Process
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- (1).Von Neumann, J. (1966). Theory of self reproducing automata, A.W. Burks ed., University of Illinois Press.Google Scholar
- (2).Demongeot, J. (1983). Coupling of Markov processes and Holley’s inequalities for Gibbs measures. Proc. of the IXth Prague Conference, 183–189, Academia, Prague.Google Scholar
- (3).Demongeot, J. (1985). Random automata and random fields. Dynamical systems and cellular automata, 99–110, Academic Press, New York.Google Scholar
- (4).Geman, S. and Geman, D. (1983). Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, preprint Brown University.Google Scholar
- (5).Hammersley, J.M. and Clifford, P. (1971). Markov fields on finite graphs and lattices, unpublished.Google Scholar
- (7).Fricot, J. (1985). Champs aléatoires de renouvellement, Thesis, GrenobleGoogle Scholar
- (9).Grenander, U. (1983). Tutorial in pattern theory, preprint Brown University.Google Scholar