Markov Random Field

A Markov Random Field ( MRF short ) or Markov network is a named after the mathematician A. Markov statistical model, which (for example, the orientation of elementary magnets ) describes undirected relationships in a field. The field consists of cells that contain random variables and spatially limited (see time limits in a Markov chain ) mutually interact.

The model is derived from the Ising model of statistical physics, which describes magnetism in solids. MRFs are closely related to Conditional Random Fields, but distinguished by the locally limited influence of the probabilities.

Application

MRFs can be used for segmentation of digital images or classified areas. In this case, for example, in a binary classification assumes that each element of the array has a force on the adjacent cells, and thus a plurality of adjacent cells of a class affect a single cell of a different class such that its classification to the class of the majority of the adjacent cells shifted will. MRFs are therefore an extension of the classic Markov chain in two or more dimensions. This allows a simple implementation of an array.