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Concept
Graph cuts in computer vision
Résumé
As applied in the field of computer vision, graph cut optimization can be employed to efficiently solve a wide variety of low-level computer vision problems (early vision), such as , the stereo correspondence problem, , object co-segmentation, and many other computer vision problems that can be formulated in terms of energy minimization. Many of these energy minimization problems can be approximated by solving a maximum flow problem in a graph (and thus, by the max-flow min-cut theorem, define a minimal cut of the graph). Under most formulations of such problems in computer vision, the minimum energy solution corresponds to the maximum a posteriori estimate of a solution. Although many computer vision algorithms involve cutting a graph (e.g., normalized cuts), the term "graph cuts" is applied specifically to those models which employ a max-flow/min-cut optimization (other graph cutting algorithms may be considered as graph partitioning algorithms).
"Binary" problems (such as denoising a ) can be solved exactly using this approach; problems where pixels can be labeled with more than two different labels (such as stereo correspondence, or denoising of a grayscale image) cannot be solved exactly, but solutions produced are usually near the global optimum.
The theory of graph cuts used as an optimization method was first applied in computer vision in the seminal paper by Greig, Porteous and Seheult of Durham University. Allan Seheult and Bruce Porteous were members of Durham's lauded statistics group of the time, led by Julian Besag and Peter Green, with the optimisation expert Margaret Greig notable as the first ever female member of staff of the Durham Mathematical Sciences Department.
In the Bayesian statistical context of smoothing noisy (or corrupted) images, they showed how the maximum a posteriori estimate of a can be obtained exactly by maximizing the flow through an associated image network, involving the introduction of a source and sink. The problem was therefore shown to be efficiently solvable.
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