The effect of stable points on the convergence of Markov random fields

The convergence rate of processes governed by simulated annealing (SA) continues to be a topic of intense research. It has often been reported how the final labeling pattern in image segmentation using Markov random fields is sensitive to the temperature schedule used. We describe the effect of introducing stable points into the initial labeling array. The stable points are seen to eliminate the dependence of the terminal point of the sample path on the temperature schedule, in addition to improving the stability of the phase transition temperature. A theorem is proved concerning the effect of the stable points on the class structure of the SA Markov chain and a conjecture is stated on the existence of an optimal set of stable points. Finally some directions for future research are discussed