Markov random field

Summary

A Markov random field is a family of random variables indexed by the vertices of an undirected graph. Each variable depends on the others only through its neighbours. It is the undirected kind of graphical model. By the Hammersley–Clifford theorem, positive Markov random fields are exactly the distributions that factor over the cliques of the graph. The Ising model and many models in image analysis are Markov random fields.