Markov random field (MRF) image segmentation algorithms have been extensively studied, and have gained wide acceptance. However, almost all of the work on them has been experimental. This provides a good understanding of the performance of existing algorithms, but not a unified explanation of the significance of each component. To address this issue, we present a theoretical analysis of several MRF image segmentation criteria. Standard methods of signal detection and estimation are used in the theoretical analysis, which quantitatively predicts the performance at realistic noise levels. The analysis is decoupled into the problems of false alarm rate, parameter selection (Neyman-Pearson and receiver operating characteristics), detection threshold, expected a priori boundary roughness, and supervision. Only the performance inherent to a criterion, with perfect global optimization, is considered. The analysis indicates that boundary and region penalties are very useful, while distinct-mean penalties are of questionable merit. Region penalties are far more important for multispectral segmentation than for greyscale. This observation also holds for Gauss-Markov random fields, and for many separable within-class PDFs. To validate the analysis, we present optimization algorithms for several criteria. Theoretical and experimental results agree fairly well.

Several multiscale objective functions for the direct segmentation of tomographic images are presented. Standard methods of signal detection and estimation are used to develop a theoretical performance analysis, which quantitatively predicts the performance at realistic noise levels. The analysis compares the relative merit of multiscale and monoscale segmentation, and shows the impact of the Shepp-Logan skull's quantization error.>