The authors consider the problem of edge detection and image estimation in nonstationary images corrupted by additive Gaussian noise. The noise-free image is represented using the compound Gauss-Markov random field developed by F.C. Jeng and J.W. Woods (1990), and the problem of image estimation and edge detection is posed as a maximum a posteriori estimation problem. Since the a posteriori probability function is nonconvex, computationally intensive stochastic relaxation algorithms are normally required. A deterministic relaxation method based on mean field annealing with a compound Gauss-Markov random (CGMRF) field model is proposed. The authors present a set of iterative equations for the mean values of the intensity and both horizontal and vertical line processes with or without taking into account some interaction between them. The relationship between this technique and two other methods is considered. Edge detection and image estimation results on several noisy images are included.