The theory of graph cuts, was first applied in Computer vision in the paper by Greig, Porteous and Seheult of Durham University, UK, as referenced below.
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 -colour problem remains unsolved for 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.
References
- J.E. Besag (1986), On the statistical analysis of dirty pictures (with discussion), Journal of the Royal Statistical Society Series B, 48, 259 - 302.
- G. Funka-Lea, Y. Boykov, C. Florin, M. P. Jolly, R. Moreau-Gobard, R. Ramaraj and D. Rinck (2006), "Automatic heart isolation for CT coronary visualization using graph cuts", IEEE International Symposium on Biomedical Imaging, 614 - 617.
- D. Geman and S. Geman (1984), Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images, IEEE Trans. Pattn Anal. Mach. Intell., 6, 721 - 741.
- D.M. Greig, B.T. Porteous and A.H. Seheult (1989), Exact maximum a posteriori estimation for binary images, Journal of the Royal Statistical Society Series B, 51, 271 - 279.