A sequence-based generalization of mean-field annealing using the Forward/Backward algorithm: Application to image segmentation

Mean-field annealing (MFA) is widely used for optimization tasks involving the determination of a set of discrete-valued assignment variables. One way of deriving MFA is via maximum entropy (ME), where one seeks the joint distribution over the (random) assignments subject to an average level of cost. MFA is obtained by assuming the individual assignments are independent. Here we propose an MFA extension for problems defined on the pixel sites of an image. Rather than introducing variables for individual sites, we represent label choices for an entire image row (or column). We then make the less restrictive assumption of independent row (rather than pixel) labelings. While it is not possible to explicitly evaluate the row labeling distribution, we can, via a Forward/Backward algorithm, explicitly evaluate sums over this distribution, to obtain a posteriori probabilities at individual sites. It turns out that the site probabilities, in turn, determine (updated) row labeling probabilities. Thus, the Forward/Backward algorithm forms the basis of an iteration, applied to the rows(columns) of the image, that yields optimized a posteriori site probabilities. This iterative method descends in the ME Lagrangian/free energy. Our method was applied to segmentation of synthetic, noise-corrupted Markov random field images. It achieved substantial reduction in misclassification rates, compared with both ICM and standard MFA.