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Edge postprocessing using probabilistic relaxation

In this paper, we develop the theory of probabilistic relaxation when the objects to be labeled are arranged in a rectangular grid with known adjacency relations. In this case a dictionary of permissible label configurations is available. The novelty of this work lies in the inclusion of measurements concerning binary relations between the objects to be labeled. These are compared with the corresponding binary relations between the nodes of the dictionary. This way, one of the major objections to probabilistic relaxation, namely, the disregard of the data after the initial assignment of probabilities, is removed. The theory we develop is demonstrated by applying it to the problem of edge relaxation labeling. We show that the inclusion of binary relations greatly improves the performance of algorithms of this kind and compare our approach with previously developed dictionary based approaches, both theoretically and experimentally. Also, a comparison with other edge-postprocessing strategies is provided.