
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
Laurent Younes, "Synchronous Random Fields and Image Restoration," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 20, no. 4, pp. 380390, April, 1998.  
BibTex  x  
@article{ 10.1109/34.677263, author = {Laurent Younes}, title = {Synchronous Random Fields and Image Restoration}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {20}, number = {4}, issn = {01628828}, year = {1998}, pages = {380390}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.677263}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Synchronous Random Fields and Image Restoration IS  4 SN  01628828 SP380 EP390 EPD  380390 A1  Laurent Younes, PY  1998 KW  Random fields KW  image processing KW  parallelism KW  MonteCarlo sampling. VL  20 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
Abstract—We propose a general synchronous model of lattice random fields which could be used similarly to Gibbs distributions in a Bayesian framework for image analysis, leading to algorithms ideally designed for an implementation on massively parallel hardware. After a theoretical description of the model, we give an experimental illustration in the context of image restoration.
[1] R. Azencott, "Image Analysis and Markov Random Fields," Proc. Int'l Conf. Ind. and Applied Mathematics, SIAM, Paris, 1987.
[2] R. Azencott, "Synchronous Boltzmann Machines and Gibbs Fields," Neurocomputing, F. FogelmanSouliéand J. Hérault, eds., NATO ASI Series, vol. F68, pp. 5163.Berlin: SpringerVerlag, 1990.
[3] R. Azencott, "HighOrder Interactions and Synchronous Learning," Proc. Stochastic Models, Statistical Methods and Algorithms in Image Analysis," P. Barone, A. Frigessi, and M. Piccioni, eds., Lecture Notes in Statistics, vol. 74, pp. 1445.Berlin: SpringerVerlag, 1992.
[4] R. Azencott, A. Doutriaux, and L. Younes, "Synchronous Boltzmann Machines and Curve Identification Tasks," Network: Computations in Neural Networks, vol. 4, pp. 461480, 1993.
[5] J. Besag, "Spatial Interaction and the Statistical Analysis of Lattice Systems," J. Royal Statistics Soc., vol. B36, pp. 192236, 1974.
[6] J. Besag and P. Green, "Spatial Statistics and Bayesian Computation," J. Royal Statistics Soc., vol. B55, pp. 2537, 1993.
[7] D.A. Dawson, "Synchronous and Asynchronous Reversible Markov Systems, Canadian Math. Bulletin, vol. 17, pp. 633649, 1975.
[8] R.L. Dobrushin, "Prescribing a System of Random Variables by Conditional Distributions," Thry. Prob. Appl., vol. 15, pp. 458486, 1970.
[9] O. François, "Ergodicitédes processus neuronaux," C. Rendus. Acad. Sci. Paris t310 Série, vol. 1, pp. 435440, 1990.
[10] A. Frigessi, C.R. Hwang, and L. Younes, "Optimal Spectral Structure of Reversible Stochastic Matrices, Monte Carlo Methods and the Simulation of Markov Random Fields," Annals of Applied Probability, 1990.
[11] D. Geman, "Random Fields and Inverse Problems in Imaging," Proc. Ecole détéde SaintFlour," Lecture Notes Mathematics, vol. 1,427. New York: Springer Verlag, 1991.
[12] D. Geman and S. Geman, "Stochastic Relaxation, Gibbs Distribution and Bayesian Restoration of Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 6, pp 721741, 1984
[13] S. Geman, A. Kehagias, and H. Künsch, "Hidden Markov Random Fields," Ann. Applied Prob., vol. 5, pp. 577602, 1995.
[14] C.J. Geyer and E.A. Thompson, "Constrained Monte Carlo Maximum Likelihood for Dependent Data (With Discussion)," J. Royal Statistical Soc., vol. B54, 657699.
[15] J. Goutsias, "Unilateral Approximation of Gibbs Random Field Images," CVGIP: Graphical Models and Image Processing, vol. 53, no 3, pp. 240257, 1991.
[16] O. Koslov and N. Vasilyev, "Reversible Markov Chains With Local Interactions," Multicomponent Random Systems, R.L. Dobrushin and Ya. G. Sinai, eds., pp. 415469.New York: Dekker, 1980.
[17] H. Künsch, "Time Reversal and Stationary Gibbs Measures," Stochastic Processes and Applications, vol. 17, pp. 159166, 1984.
[18] J.L. Lebowitz, C. Maes, and E. Speer, "Statistical Mechanics of Probabilistic Cellular Automata," J. Stat. Physics, vol. 59, pp. 117170, 1990.
[19] W.A. Little, "The Existence of Persistent States in the Brain," Math. Biosci., vol. 19, pp. 101120, 1974.
[20] C. Maes and S.B. Shlosman, "Ergodicity of Probabilistic Cellular Automata: A Constructive Criterion," Comm. Stat. Phys., vol. 135, pp. 233251, 1989.
[21] P. Peretto and J.J. Niez, "Collective Properties of Neural Networks," Disordered Systems and Biological Organisation (Les Houches 1985), pp. 171185, E. Bienenstock et al. eds., Berlin: Springer Verlag, 1986.
[22] T. Poggio, E.B. Gamble, J.J. Little, "Parallel Integration of Vision Modules," Science, vol 242, pp. 436440, 1988.
[23] J.G. Propp and D.B. Wilson, Exact Sampling With Coupled Markov Chains and Applications to Statistical Mechanics. Preprint, Massachusetts Institute of Tech nology, 1996.
[24] A.F.M. Smith and G.O. Roberts, "Bayesian Computation Via the Gibbs Sampler and Related Markov Chain Monte Carlo Methods," J. Royal Statistics Soc., vol. B55, pp. 323, 1993.
[25] A. Sokal, "Monte Carlo Methods in Statistical Mechanics: Foundations and New Algorithms," Cours de troisième cycle de la physique en Suisse romande. Lausanne, 1989.
[26] R.H. Swendsen and J.S. Wang, "Nonuniversal Critical Dynamics in Monte Carlo Simulations," Phys. Rev. Lett., vol. 58, pp. 8688, 1987.
[27] A. Trouvé, "Partially Parallel Simulated Annealing: Low and High Temperature Approach of the Invariant Measure," Proc. USFrench Workshop Applied Stochatic Analysis, I. Karatzas and D. Ocone, eds., Lecture Notes Control and Information Sciences, vol. 177, Springer Verlag, 1992.
[28] L. Younes, "Parameter Estimation for Imperfectly Observed Gibbsian Fields," Prob. Theory and Rel. Fields, vol. 82, pp. 625645, 1989.
[29] L. Younes, "Parameter Estimation for Imperfectly Observed Gibbs Fields and Some Comments on Chalmond's EM Gibssian Algorithm," Proc. Stochastic Models, Statistical Methods and Algorithms in Image Analysis, P. Barone, A. Frigessi and M. Piccioni, eds. Lecture Notes in Statistics, vol. 74, pp. 1445.Berlin: SpringerVerlag, 1992.
[30] L. Younes, "Representation of Gibbs Fields With Synchronous Random Fields," Markov Processes and Related Fields, vol. 2, pp. 285316, 1996.
[31] L. Younes, "Synchronous Boltzmann Machines Can Be Universal Estimators," Applied Math. Letters, vol. 9, no. 3, pp. 109113, 1996.