On the estimation of noisy binary Markov random fields

摘要

Possolo (Technical Report No. 77, Department of Statistics GN-22, University of Washington, Seattle (1986)) and Derin and Elliott (IEEE Trans. Pattern Analysis Mach. Intell.PAMI-9, 39–55 (1987)) proposed, for the estimation of binary and more general m-ary Markov random fields, the “logit” method, based on histogramming an image. The authors applied the method to noise-free Markov random fields. For estimation of noisy images, one might recursively implement the logit method within an iterative restoration algorithm, such as the iterated conditional modes (ICM) method of Besag (J. R. Statist. Soc. B48, 259–302 (1986)), by alternating parameter estimation and restoration. It is noted that failure to smooth zero histogram counts, for the purposes of estimation, can cause ICM to cycle indefinitely.