In this section, we consider the class of 2-D non-causal models called the Gaussian Markov random field (GMRF) models described in [6], [12], [21], and [46]. Pixel gray levels have joint Gaussian distributions and correlations controlled by a number of parameters representing the statistical dependence of a pixel value on the pixel values in a symmetric neighborhood. There are two basic schemes for generating a GMRF image model, both of which are discussed in [6].