Markov Random Fields

  • Luis Enrique SucarEmail author
Part of the Advances in Computer Vision and Pattern Recognition book series (ACVPR)


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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Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

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

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