A simulation-based estimator for hidden Markov random fields

An estimator for estimating the parameters of a Markov random field X from inaccurate observations is introduced. The author considers first a Markov (Gibbs) random field X=(X/sub i,j/) on a lattice L=((i,j): i=1,2,. . .,n; j=1,2,. . .,m). The marginal distributions of (X/sub i,j/,X/sub i+u,j+v/) (u,v=-1,0,1) are first estimated from an image. Then, random fields X* are simulated with the probability of X*/sub i+u,j+v/)=b nearly equal to the estimate of P(X/sub i,j/=X/sub i+u/,=b). A simulation method similar to the Gibbs sampler is used. The parameters of the Markov random field model are estimated from the X*'s with the pseudolikelihood method.<
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