Markov Random Fields

Chapter
Part of the Advances in Computer Vision and Pattern Recognition book series (ACVPR)

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.

References

  1. 1.
    Besag, J.: Statistical analysis of non-lattice data. Statistician 24(3), 179–195 (1975)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Binder, K.: Ising Model. Hazewinkel, Michiel, Encyclopedia of Mathematics. Springer, New York (2001)Google Scholar
  3. 3.
    Geman, D., Geman, S., Graffigne, C.: Locating Object and Texture Boundaries. Pattern recognition theory and applications. Springer, Heidelberg (1987)CrossRefGoogle Scholar
  4. 4.
    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 Unpublished Paper.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
  5. 5.
    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)Google Scholar
  6. 6.
    Hernández-Gracidas, C., Sucar, L.E., Montes, M.: Improving image retrieval by using spatial relations. J. Multimed. Tools Appl. 62, 479–505 (2013)CrossRefGoogle Scholar
  7. 7.
    Kindermann, R., Snell, J.L.: Markov random fields and their applications. Am. Math. Soc. 34, 143–167 (1980)Google Scholar
  8. 8.
    Lafferty, J., McCallum, A., Pereira, F.: Conditional random fields: probabilistic models for segmenting and labeling sequence data. In: International Conference on Machine Learning (2001)Google Scholar
  9. 9.
    Li, S.Z.: Markov Random Field Modeling in Image Analysis. Springer, London (2009)MATHGoogle Scholar
  10. 10.
    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)Google Scholar
  11. 11.
    Wallach, H.M.: Conditional random fields: an introduction. Technical Report MS-CIS-04-21, University of Pennsylvania (2004)Google Scholar

Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  1. 1.Instituto Nacional de Astrofísica, Óptica y Electrónica (INAOE)Santa María TonantzintlaMexico

Personalised recommendations