MEAN-FIELD ANNEALING USING COMPOUND GAUSS-MARKOV RANDOM-FIELDS FOR EDGE-DETECTION AND IMAGE ESTIMATION

In this paper, we consider the problem of edge detection and image est imation in nonstationary images corrupted by additive Gaussian noise. The noise-free image is represented using the compound Gauss-Markov ra ndom field of Jeng and Woods and the problem of image estimation and e dge detection is posed as a maximum a posteriori estimation problem. S ince the a posteriori probability function is nonconvex, computational ly intensive stochastic relaxation algorithms are normally required. W e propose a deterministic relaxation method based on mean field anneal ing with a compound Gauss-Markov random (CGMRF) field model. We presen t a set of iterative equations for the mean values of the intensity an d both horizontal and vertical line processes with or without taking i nto account some interaction between them. We show the relationship be tween this technique and two other methods, that described by Geiger a nd Girosi and the one proposed by Simchony et al. Finally, we present edge detection and image estimation results on several noisy images.