Markov Random Field
A Markov Random Field ( MRF for short ) or Markow network is a statistical model named after the mathematician A. Markow , which describes undirected relationships (e.g. the alignment of elementary magnets ) in a field . The field consists of cells which contain random variables and which are spatially limited (cf. temporal limitation in a Markov chain ) and interact with one another.
The model is a generalization of the Ising model of statistical physics , which describes magnetism in solids. In addition to the Ising model, conditional random fields also belong to the class of Markov random fields. With the help of Markov Random Fields, relationships can be represented that cannot be described by Bayesian networks , for example cyclical dependencies. Conversely, however, these can also represent relationships that cannot be described in Markov Random Fields. The formal properties of an MRF include the Global Markov Property: Each node (as a representative of the random variable) is independent of all other nodes if all of its neighbors are given.
application
MRFs can be used to segment digital images or classified areas. In the case of a binary classification, for example, it is assumed that each element of the field has a force effect on the neighboring cells and thus several neighboring cells of one class influence a single cell of another class in such a way that their classification shifts to the class of the majority of the neighboring cells becomes. MRFs are thus an extension of the classic Markov chain in two or more dimensions. This enables easy implementation as an array .
literature
- Ross Kindermann: Markov Random Fields and Their Applications . Contemporary Mathematics. American Mathematical Society, Providence 1980, ISBN 978-0-8218-5001-5 ( ams.org ).