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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 converted into a 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. See the references below.
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. Their approach is often applied iteratively to a sequence of binary images, usually yielding near optimal solutions. See the article by Funka-Lea at al, as referenced below, for a recent application.
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