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In the Bayesian statistical context of [[smoothing]] noisy, or corrupted, images, Greig, Porteous and Seheult showed how the maximum a posteriori estimate of a binary image can be obtained ''exactly'' by maximising the flow through an associated image network, involving the introduction of a ''source'' and ''sink''. The problem was therefore shown to be a non NP hard problem which could be solved using known efficient [[algorithms]].
Prior to this result, ''approximate'', although more general, techniques such as [[simulated annealing]], as proposed by the Geman brothers, or iterated conditional modes, a type of [[greedy algorithm]] as suggested by Julian Besag, were used to solve these types of problems.
Although the general <math>k</math>-colour problem remains unsolved for <math>k > 2,</math> the approach of Greig, Porteous and Seheult has turned out to have wide applicability in general computer vision problems. See Boykov, Veksler and Zabih. Greig, Porteous and Seheult approaches are often applied iteratively to a sequence of binary problems, usually yielding near optimal solutions. See the article by Funka-Lea at al for a recent application.
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