Digital Video Processing, Second Edition

Appendix C. Markov and Gibbs Random Fields

Markov random fields (MRFs) specified in terms of Gibbs distributions have become popular as a priori models in Bayesian formulations for image-processing applications such as texture modeling and generation [Cro 83, Che 93], image segmentation and restoration [Gem 84, Der 87, Pap 92], and motion estimation [Dub 93]. This appendix provides the definitions of an MRF and the Gibbs distribution and then describes their relationship by using the Hammersley–Clifford theorem. The specification of MRFs in terms of Gibbs distributions has led to the term “Gibbs random field” (GRF). We also discuss how to obtain the local (Markov) conditional pdfs from the Gibbs distribution, which is a joint pdf.

C.1 Equivalence ...