Random field Guide, Meaning , Facts, Information and Description
In
probability theory, let
S = {
X1, ...,
Xn}, with the
Xi in {0,1,...,
G-1}, be a set of
random variables on the
sample space Ω={0,1,...,
G-1}
n, a probability measure π is a
random field if
- .
There exist several types of random fields, such as
Markov random field (MRF) and
Gibbs random field (GRF). A MRF exhibits the Markovian property
- ,
where is a set of neighbours of the random variable . In other words, the probability a random variable assumes a value does not depend on all of the random variables.
A probability of a random variable in a MRF is showed by the equation 1, Ω' is the same realization of Ω, except for random variable . It is easy to see that it is difficult to calculate with this equation. The solution to this problem was proposed by Besag in 1974, when he made a relation between MRF and GRF.
Reference
- Besag, J. E. Spatial Interaction and the Statistical Analysis of Lattice Systems. Journal of Royal Statistical Society: Series B 36, 2 (May 1974), 192-236.
See Also
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