This paper investigates the theoretical limits of probabilistic relaxation labeling (PRL), applied to per-pixel contextual image classification. The performance of a scheme which is defined to be optimal (within a class of PRL schemes) is studied, and found to fall short of that theoretically obtainable by directly considering all the original a posteriori probabilities (PPs) in the image. Lt is also found that an optimal scheme must use different updating functions at each iteration, and that these functions will depend on the distributions of the original per-pixel data. An estimation based implementation of the optimal scheme — termed 'trained probabilistic relaxation' (TPR) is then described, which, in spite of it's theoretical limitations, has a number of commendabl
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