This paper presents an algorithm for segmenting an image that is composed of an unknown number of regions c. In each region n, the image data gn are viewed as a realization from a homogeneous parametric random field with a class conditional density function p(gn|γn), where γnis an unknown parameter set. The number of regions c and the segmentation Sc are treated as unknown constants that are estimated using the maximum likelihood (ML) estimation principle. The ML estimates for c and Sc are obtained by maximizing log{p(g|Sc)} over all possible c and Sc. p(g|Sc) has the desirable property of unbiasedness; i.e., ES{log{p(g|Sc)}} ≤ ES {log{p(g|Sctrue)}. Unfortunately, it suffers from two limitations: (i) a closed-form analytic expression for p(g|Sc) for a given fixed c cannot be obtained in general, and (ii) in order to arrive at the optimum (c*, Sc*) we must evaluate p(g|Sc) for all possible c and Sc, a most formidable task. This paper presents a solution to both problems that results into an optimum number of classes c*; an "optimum" window-based coarse segmentation Sc* of the image; and a ML estimate of the parameters ΓS = (γ1, γ2, ..., γc) of the c* regions induced by Sc*. From this knowledge, the mixed windows (windows that fall between regions) are segmented further in a supervised mode (known parameter case) using the ML high-resolution segmentation developed by Cohen and Cooper (IEEE Trans. Pattern Anal. Mach. Intelligence Mar., 1987). The ML algorithm is applied to the problem of unsupervised segmentation of textured images of natural outdoor scenes. © 1992.
