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Strong Markov Random Field Model

R. Paget
IEEE Transactions on Pattern Analysis and Machine Intelligence
Vol. 26, No. 3, pp. 408-413, March 2004

Abstract

The strong Markov random field (strong-MRF) model is a submodel of the more general MRF-Gibbs model. The strong-MRF model defines a system whose field is Markovian with respect to a defined neighborhood, and all subneighborhoods are also Markovian. A checkerboard pattern is a perfect example of a strong Markovian system. Although the strong Markovian system requires a more stringent assumption about the field, it does have some very nice mathematical properties. One mathematical property is the ability to define the strong-MRF model with respect to its marginal distributions over the cliques. Also, a direct equivalence to the Analysis-of-Variance (ANOVA) log-linear construction can be proven. From this proof, the general ANOVA log-linear construction formula is acquired.


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@Article{eth_biwi_00291,
  author = {R. Paget},
  title = {Strong Markov Random Field Model},
  journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
  year = {2004},
  month = {March},
  pages = {408-413},
  volume = {26},
  number = {3},
  keywords = {Markov processes, Contingency table analysis, Nonparametric statistics, Texture, Model development}
}