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Hidden Markov Random Field Model
Let
and
be two alphabets:
Let
be the set of indices and
denote any family of random variables
indexed by
,
in which each random variable R_{i} takes
a value z_{i} in its state space. Such a family R is called a
random field. The joint event
is
simplified to R=r where
is a
configuration of R, corresponding to a realization of
this random field. Let X and Y be two such random fields whose
state spaces are
and
respectively so
that for
we have
and
.
Let x denote a configuration
of X and
be the set of all possible configurations
so that
Similarly, let y be a configuration of Y and
be the set of all possible configurations so that
Given ,
Y_{i} follows a conditional probability
distribution

(1) 
where
is the set of parameters. For all ,
the
function family
has the same known analytic
form. We also assume that (X, Y) is pairwise independent,
meaning

(2) 
In order to develop the HMRF model we firstly take the standard FM
model as a comparison.
Next: Finite Mixture Model
Up: Segmentation of Brain MR
Previous: Introduction
Yongyue Zhang
20000511