C. 5. Problemas-inversos-y-reconstruccin-bayesiana-modelo-de-interaccin-de-reas-de-baddeley-van-lieshout, Estos modelos penalizarn la agregacin injustificada de granos. Verificamos as que la reconstruccin por MAP no presenta estos defectos de las respuestas mltiples. En [105], el autor utiliza, tanto para la simulacin, como para la optimizacin, una dinmica de procesos de nacimiento y muerte (PNM, [76]). Esta dinmica se define sobre la imagen discretizada. Para la optimizacin por recocido simulado, van Lieshout establece una condicin suficiente sobre el esquema de temperaturas para asegurar la convergencia

. Permiten-controlar-la-convergencia-de-las-simulaciones, El problema de convergencia del recocido simulado en este espacio sigue abierto Sin embargo, la experiencia muestra que una buena aplicacin del recocido simulado sobre un espacio de estados E ? R p continua " funcionando bien

. Sobre-un-arreglo-triangular-plano, considrese el campo de Markov binario invariante por traslacin con 6 v.m.c.. Describa las claques, los potenciales, las distribuciones condicionales. Identificar los submodelos: isotrpico; reversible (?A, ? A (x A ) es invariante por permutacin de los ndices de x en A)

D. Aldous and P. Et-diaconis, Shuffling Cards and Stopping Times, The American Mathematical Monthly, vol.93, issue.5, pp.333-348, 1986.
DOI : 10.2307/2323590

D. Aldous and J. Et-fill, Reversible Markov chains and random walks on graphs, Monograph in preparation, 1993.

Y. Amit and U. Et-grenander, Comparing sweep strategies for stochastic relaxation, Journal of Multivariate Analysis, vol.37, issue.2, pp.197-222, 1991.
DOI : 10.1016/0047-259X(91)90080-L

R. Azencott and . Ed, Simulated annealing : Parallelization techniques, 1992.

A. Baddeley and M. N. Van-lieshout, Area-interaction point processes, Annals of the Institute of Statistical Mathematics, vol.52, issue.4, pp.601-619, 1995.
DOI : 10.1007/BF01856536

A. J. Baddeley and J. Et-moller, Nearest-neighbour Markov point processes, Ann. Inst. Stat. Math, vol.57, pp.89-121, 1989.
DOI : 10.2307/1403381

A. A. Barker, Monte Carlo calculations of the radial distribution functions for a proton-electron plasma, Austr, J. Phys, vol.18, pp.119-133, 1965.

S. Bayomog, X. Guyon, and C. Et-hardouin, Markov Chain Markov Field Dynamic, Preprint SAMOS, n ? 100, p.25, 1998.

J. Besag, Spatial interaction and the statistical analysis of lattice systems, JRSS B, vol.36, pp.192-236, 1974.

J. Besag, Statistical analysis of dirty pictures*, Journal of Applied Statistics, vol.6, issue.5-6, p.318, 1986.
DOI : 10.1016/0031-3203(83)90012-2

P. Brodatz, Texture : a photographic album for artists ans designers, 1966.

D. S. Carter and P. M. Et-prenter, Exponential spaces and counting processes, Exponential states and counting processes, pp.1-19, 1972.
DOI : 10.1007/BF00535104

O. Catoni, Rough Large Deviation Estimates for Simulated Annealing: Application to Exponential Schedules, The Annals of Probability, vol.20, issue.3, pp.1109-1146, 1992.
DOI : 10.1214/aop/1176989682

B. Chalmond, Elments de modlisation pour l'analyse d'image, p.96

D. Chauveau, J. Dibolt, and C. P. Et-robert, Control by the Central Limit Theorem, Discrtisation and MCMC convergence assessement, pp.99-126, 1998.
DOI : 10.1007/978-1-4612-1716-9_5

G. R. Cross and A. K. Et-jain, Markov Random Field Texture Models, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.5, issue.1, pp.25-39, 1983.
DOI : 10.1109/TPAMI.1983.4767341

L. Devroye, Non-Uniform random variable generation, 1986.
DOI : 10.1007/978-1-4613-8643-8
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.333.8896

P. Diaconis and M. Et-sahshahani, Generating a random permutation with random transpositions, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.50, issue.2, pp.159-179, 1981.
DOI : 10.1007/BF00535487

P. Diaconis and M. Et-shahshahani, Time to Reach Stationarity in the Bernoulli???Laplace Diffusion Model, SIAM Journal on Mathematical Analysis, vol.18, issue.1, pp.208-218, 1987.
DOI : 10.1137/0518016

P. Diaconis, R. Graham, and J. Et-morrison, Asymptotic analysis of a random walk on a hypercube with many dimensions, Random Structures and Algorithms, vol.76, issue.1, pp.51-72, 1990.
DOI : 10.1002/rsa.3240010105

P. Diaconis and L. Et-saloff-coste, What do we know about the Metropolis algorithm ?, Proc. of the Twenty-Seventh Annual ACM Symp. on the Theo. Comp, pp.112-129, 1995.

P. Diaconis, The cutoff phenomenon in finite Markov chains., Proc. Natl. Acad. Sci. USA, pp.1659-1664, 1996.
DOI : 10.1073/pnas.93.4.1659

J. M. Dinten, Tomographiè a partir d'un nombre limit de projections: rgularisation par champs markoviens, 1990.

L. R. Dobrushin, Central Limit Theorem for Nonstationary Markov Chains. I, Theory of Probability & Its Applications, vol.1, issue.1, pp.65-80, 1956.
DOI : 10.1137/1101006

W. Doeblin, Expos de la thorie des cha??nescha??nes simples constantes de MarkovàMarkovà nombre fini d'tats, Rev, Math. Union Interbalkan, vol.2, pp.77-105, 1938.

P. Doukhan, Mixing : Properties and Examples, L.N.S. n ?, vol.85, 1995.

W. Feller, An introduction to probability theory and its applications, 1968.

J. A. Fill, An interruptible algorithm for perfect simulation via Markov chains, Ann. Appl. Proba, vol.8, pp.131-162, 1998.

S. G. Foss and R. L. Et-tweedie, Perfect simulation and backward coupling, Stochastic models, pp.187-203, 1998.

A. Frigessi, C. R. Hwang, D. Stephano, P. Sheu, and S. J. , Convergence rates of Gibbs sampler, the Metropolis algorithm and other single-site updating dynamics, J.R.S.S. B, vol.55, pp.205-219, 1993.

C. Gaetan, A stochastic algorithm for maximun likelihood estimation of Gibbs point processes, 1994.

N. Gantert, Laws of large numbers for the annealing algorithm, Stochastic Processes and their Applications, vol.35, issue.2, pp.309-313, 1989.
DOI : 10.1016/0304-4149(90)90009-H

F. R. Gantmacher, Applications of the theory of Matrices Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, Geman D. et Geman S, vol.37, issue.6, pp.721-741, 1959.

D. Geman and S. Et-geman, Relaxation and annealing with constraints, Div. Appl. Maths, 1987.

D. Geman, Random fields and inverse problems in imaging, L.N.M. n ?, vol.9, 1990.
DOI : 10.1109/TPAMI.1987.4767898

S. Geman and C. Et-graffigne, Markov random field models and their application in computer vision, Proc. Int. Congress of Maths, pp.1496-1517, 1986.

H. O. Georgii, Gibbs measure and phase transitions, 1988.
DOI : 10.1515/9783110850147

B. Gidas, Metropolis-type Monte Carlo simulation algorithms and simulated annealing ; Trends in Contemporary Probability, 1991.

C. Graffigne, Experiments in texture analysis and segmentation, 1987.

D. Griffeath, A maximal coupling for Markov chains, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.3, issue.2, pp.95-106, 1975.
DOI : 10.1007/BF00539434

X. Guyon, Random Fields on a Network : Modeling, Statistics and Applications, 1995.

O. Häggström, M. N. Van-lieshout, and J. Et-møller, Characterisation results and Markov chain Monte Carlo algorithms including exact simulation for some point processes, 1999.

O. Häggström and K. Et-nelander, On Exact Simulation of Markov Random Fields Using Coupling from the Past, Scandinavian Journal of Statistics, vol.26, issue.3, 1998.
DOI : 10.1111/1467-9469.00156

B. Hajek, Cooling Schedules for Optimal Annealing, Mathematics of Operations Research, vol.13, issue.2, pp.311-329, 1988.
DOI : 10.1287/moor.13.2.311

W. K. Hastings, Monte Carlo sampling methods using Markov chains and their applications, Biometrika, vol.57, issue.1, pp.97-109, 1970.
DOI : 10.1093/biomet/57.1.97

D. L. Isaacson and R. W. Et-madsen, Markov chains; Theory and applications, 2-` eme Ed, 1985.

V. E. Johnson, Studying Convergence of Markov Chain Monte Carlo Algorithms Using Coupled Sample Paths, Journal of the American Statistical Association, vol.22, issue.433, pp.154-166, 1996.
DOI : 10.1080/01621459.1987.10478458

V. Johnson and A. Et-reutter, General strategies for assesing convergence of MCMC algorithms using coupled sample paths, 1995.

S. Karlin, A first course in stochastic processes, 1968.

J. Keilson, Markov chain models-Rarity and Exponentiality, 1979.
DOI : 10.1007/978-1-4612-6200-8

W. S. Kendall, A spatial Markov property for nearest-neighbour Markov point processes, J. Appl. Proba, vol.28, pp.767-778, 1990.
DOI : 10.2307/3214821

W. S. Kendall, Perfect Simulation for the Area-Interaction Point Process, Probability towards, pp.218-234, 1997.
DOI : 10.1007/978-1-4612-2224-8_13

W. Kendall and J. Et-møller, Perfect Metropolis-Hastings simulation of locally stable point processes, 1999.

F. P. Kelly and B. D. Et-ripley, A note on Strauss's model for clustering, Biometrika, vol.63, issue.2, pp.357-360, 1976.
DOI : 10.1093/biomet/63.2.357

. Kinderman and J. L. Snell, Markov random fields and their applications, Contemporary Maths. A.M.S, vol.1, 1980.
DOI : 10.1090/conm/001

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Optimization by Simulated Annealing, Science, vol.220, issue.4598, pp.671-680, 1983.
DOI : 10.1126/science.220.4598.671

M. Lavielle, Optimal segmentation of random processes, IEEE Transactions on Signal Processing, vol.46, issue.5, pp.1365-1373, 1998.
DOI : 10.1109/78.668798

S. Li, Markov Random Field modeling in computer vision, 1995.
DOI : 10.1007/978-4-431-66933-3

T. Lindvall, Lectures on coupling method, 1992.

D. Luenberger, Introduction to dynamical systems : Theory and Applications, 1979.

J. S. Liu, Metropolized Gibbs sampler: an improvement, 1995.

J. Marroquin, S. Mitter, and T. Et-poggio, Probabilistic Solution of Ill-Posed Problems in Computational Vision, Journal of the American Statistical Association, vol.18, issue.397, pp.76-89, 1987.
DOI : 10.1080/01621459.1987.10478393

S. Martinez and B. Et-ycart, Decaying rates and cutoff for convergence and hitting times of Markov chains, 1998.

G. Matheron, Random sets and integral geometry, 1975.

N. Metropolis, A. Rosenbluth, A. Teller, and E. Et-teller, Equation of State Calculations by Fast Computing Machines, The Journal of Chemical Physics, vol.21, issue.6, pp.1087-1092, 1953.
DOI : 10.1063/1.1699114

J. Møller, On the rate of convergence of spatial birth-and-death processes, Annals of the Institute of Statistical Mathematics, vol.39, issue.2, pp.565-581, 1989.
DOI : 10.1007/BF00050669

J. Møller, Markov chain Monte Carlo and spatial point processes Markov chain Monte Carlo and spatial point processes, Proc. Sm. Eur. de Stat., Current trend in stochastic geometry with applications, 1994.

J. Møller, Perfect simulation of conditionally specified models, Journal of the Royal Statistical Society: Series B (Statistical Methodology), vol.61, issue.1, pp.251-264, 1999.
DOI : 10.1111/1467-9868.00175

D. J. Murdoch and P. J. Et-green, Exact sampling from continuous state space, Scan, J. Stat, vol.25, pp.483-502, 1998.
DOI : 10.1111/1467-9469.00116

P. Peskun, Optimum Monte-Carlo sampling using Markov chains, Biometrika, vol.60, issue.3, pp.607-612, 1973.
DOI : 10.1093/biomet/60.3.607

J. W. Pitman, On coupling of Markov chains, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.28, issue.4, pp.315-322, 1976.
DOI : 10.1007/BF00532957

J. G. Propp and D. B. Et-wilson, Exact sampling with coupled Markov chains and applications to statistical mechanics, Random Structures and Algorithms, pp.223-251, 1996.

A. E. Raftery and S. M. Lewis, Implementing MCMC, in Markov Chain Monte-Carlo in Practice, 1996.

B. D. Ripley and F. P. Kelly, Markov Point Processes, Journal of the London Mathematical Society, vol.2, issue.1, pp.188-192, 1977.
DOI : 10.1112/jlms/s2-15.1.188

R. Ch, Mthodes de simulation en statistique, Economica, 1996.

C. P. Robert and D. Et-cellier, Convergence Control of MCMC Algorithms, Discretization and MCMC convergence assessement, pp.27-46, 1998.
DOI : 10.1007/978-1-4612-1716-9_2

C. P. Robert, Discretization and MCMC convergence assessement, L.N.S. n ?, vol.135, 1998.

L. Saloff-coste, Lectures on finite Markov chains, Ecole d't de Probabilit de St, Flour XXVI, L.N.M. n ? 1665, 1997.
DOI : 10.1007/bfb0092621

E. Seneta, Non-negative matrices, 1975.

A. Sinclair, Algorithms for random generation and counting : a Markov chain approach, 1993.
DOI : 10.1007/978-1-4612-0323-0

D. Stoyan, W. S. Kendall, and J. Et-mecke, Stochastic Geometry and Its Applications., Biometrics, vol.45, issue.2, 1995.
DOI : 10.2307/2531521

D. J. Strauss, A model for clustering, Biometrika, vol.62, issue.2, pp.467-475, 1975.
DOI : 10.1093/biomet/62.2.467

D. J. Strauss, Clustering on coloured lattices, Journal of Applied Probability, vol.1, issue.01, pp.135-143, 1977.
DOI : 10.2307/3212721

T. H. Thorisson, Coupling methods in probability theory, Scand, Jour. of Stat, vol.22, pp.159-182, 1995.

L. Tierney, Markov Chains for Exploring Posterior Distributions, The Annals of Statistics, vol.22, issue.4, pp.1701-1762, 1994.
DOI : 10.1214/aos/1176325750
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.110.5995

L. Tierney, Introduction to general state-space Markov chain theory, Markov Chain Monte Carlo in practice, pp.59-74, 1996.

L. Tierney, A note on Metropolis-Hastings kernels for general state spaces, The Annals of Applied Probability, vol.8, issue.1, 1995.
DOI : 10.1214/aoap/1027961031

A. Trouv, Paralllisation massive du recuit simul, Thèse de Doctorat, 1993.

R. L. Tweedie and M. Chains, Structure and Applications Handbook of Sta- tistics [103] van Laarhoven P Simulated annealing : Theory and Applications, Reidel Stochastic annealing for nearest-neighbour point processes with application to object recognition, J. et Aarts E. Adv. Appl. Prob, vol.26, pp.281-300, 1987.

M. N. Van-lieshout, Markov point processes and their application in hight-level imaging, Bull. ISI, pp.559-576, 1995.

G. Winkler, Image analysis, Randoms Fields and Dynamic Monte Carlo Methods: a mathematical introduction, 1995.
DOI : 10.1007/978-3-642-97522-6

J. F. Yao, On constrained simulation and optimisation by Metropolis chains, Statistics and Probability letters, 1999.

B. Ycart, Cutoff for samples of Markov chains, ESAIM Probability and Statistics, 1998.

B. Ycart, Stopping tests for Monte-Carlo Markov chains methods, 1999.

B. Ycart, Cutoff for Markov chains : some example and applications, Summer school on complex systems, 1998.
DOI : 10.1007/978-94-010-0920-1_6

L. Younes, Probì emes d'estimation paramtrique pour les champs de Gibbs Markoviens, 1988.