After the stochastic simulated annealing technique was applied in the field of image processing, there have been many research reports on the Markov random field based image processing. These MRF-based edge-preserving smoothing techniques showed good results in the field of restoration, reconstruction, edge detection, and segmentation of the images, however, they have common drawbacks. First, those methods do not work well for smoothing of the nonstationary or signal-dependent noise. In real world images, the noises are often nonstationary and signal-dependent. Second, those edge-preserving smoothing techniques employ implicit or explicit thresholds to determine the existence of the edges, and they use fixed single thresholds throughout the entire image. As a result of these drawbacks, small features in the area of low noise variance are lost or blurred in order to restore the features in the high variance area. In order to cure these problems, we need an adaptive edge-preserving smoothing method which can be applied to nonstationary or signal-dependent noise with adaptive thresholding. The adaptive mean field annealing is an adaptive version of MFA, which fulfills this purpose by taking advantage of the local nature of the MRF and the fact that nonstationary or signal-dependent noise can be approximated by locally stationary additive Gaussian noise. In AMFA, the a priori information about the noise is not necessary and, hence, the difficulty of estimating the parameters is greatly reduced.