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A.J. Gray, J.W. Kay, D.M. Titterington, "An Empirical Study of the Simulation of Various Models used for Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 5, pp. 507513, May, 1994.  
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@article{ 10.1109/34.291447, author = {A.J. Gray and J.W. Kay and D.M. Titterington}, title = {An Empirical Study of the Simulation of Various Models used for Images}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {16}, number = {5}, issn = {01628828}, year = {1994}, pages = {507513}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.291447}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
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TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  An Empirical Study of the Simulation of Various Models used for Images IS  5 SN  01628828 SP507 EP513 EPD  507513 A1  A.J. Gray, A1  J.W. Kay, A1  D.M. Titterington, PY  1994 KW  image reconstruction; Bayes methods; Markov processes; Markov random fields; Bayesian image restoration methods; moderatetolarge scale clustering; iterative algorithms; Markov mesh models; strong directional effects; parameter estimation VL  16 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
Markov random fields are typically used as priors in Bayesian image restoration methods to represent spatial information in the image. Commonly used Markov random fields are not in fact capable of representing the moderatetolarge scale clustering present in naturally occurring images and can also be time consuming to simulate, requiring iterative algorithms which can take hundreds of thousands of sweeps of the image to converge. Markov mesh models, a causal subclass of Markov random fields, are, however, readily simulated. We describe an empirical study of simulated realizations from various models used in the literature, and we introduce some new meshtype models. We conclude, however, that while largescale clustering may be represented by such models, strong directional effects are also present for all but very limited parameterizations. It is emphasized that the results do not detract from the use of Markov random fields as representers of local spatial properties, which is their main purpose in the implementation of Bayesian statistical approaches to image analysis. Brief allusion is made to the issue of parameter estimation.
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