Abstract
This chapter presents an introduction to Markov random fields (MRFs), also known as Markov networks, which are undirected graphical models. We describe how a Markov random field is represented, including its structure and parameters, with emphasis on regular MRFs. Then, a general stochastic simulation algorithm to find the optimum configuration of an MRF is described, including some of its main variants. The problem of parameter estimation for an MRF is addressed, considering the maximum likelihood estimator. Conditional random fields are also introduced. The chapter concludes with two applications of MRFs for image analysis, one for image de-noising and the other for improving image annotation by including spatial relations.
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References
Besag, J.: Statistical analysis of non-lattice data. Statistician 24(3), 179–195 (1975)
Binder, K.: Ising Model. Hazewinkel, Michiel, Encyclopedia of Mathematics. Springer, New York (2001)
Geman, D., Geman, S., Graffigne, C.: Locating Object and Texture Boundaries. Pattern recognition theory and applications. Springer, Heidelberg (1987)
Hammersley, J.M., Clifford, P.: Markov fields on finite graphs and lattices. Unpublished Paper. http://www.statslab.cam.ac.uk/grg/books/hammfest/hamm-cliff.pdf (1971). Accessed 14 Dec 2014
Hernández-Gracidas, C., Sucar, L.E.: Markov random fields and spatial information to improve automatic image annotation. Advances in Image and Video Technology. Lecture Notes in Computer Science, vol. 4872, pp. 879–892. Springer (2007)
Hernández-Gracidas, C., Sucar, L.E., Montes, M.: Improving image retrieval by using spatial relations. J. Multimed. Tools Appl. 62, 479–505 (2013)
Kindermann, R., Snell, J.L.: Markov random fields and their applications. Am. Math. Soc. 34, 143–167 (1980)
Lafferty, J., McCallum, A., Pereira, F.: Conditional random fields: probabilistic models for segmenting and labeling sequence data. In: International Conference on Machine Learning (2001)
Li, S.Z.: Markov Random Field Modeling in Image Analysis. Springer, London (2009)
Sutton, C., McCallum, A.: An Introduction to Conditional Random Fields for Relational Learning. In: Geetor, L., Taskar, B. (eds.) Introduction to Statistical Relational Learning, MIT Press, Cambridge (2006)
Wallach, H.M.: Conditional random fields: an introduction. Technical Report MS-CIS-04-21, University of Pennsylvania (2004)
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Sucar, L.E. (2015). Markov Random Fields. In: Probabilistic Graphical Models. Advances in Computer Vision and Pattern Recognition. Springer, London. https://doi.org/10.1007/978-1-4471-6699-3_6
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DOI: https://doi.org/10.1007/978-1-4471-6699-3_6
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