Graph Cuts and Efficient N-D Image Segmentation

Yuri Boykov, Gareth Funka-Lea

In International Journal of Computer Vision (IJCV), vol. 70, no. 2, pp. 109-131, November, 2006 (accepted in 2004).


Combinatorial graph cut algorithms have been successfully applied to a wide range of problems in vision and graphics. This paper focusses on possibly the simplest application of graph-cuts: segmentation of objects in image data. Despite its simplicity, this application epitomizes the best features of combinatorial graph cuts methods in vision: global optima, practical efficiency, numerical robustness, ability to fuse a wide range of visual cues and constraints, unrestricted topological properties of segments, and applicability to N-D problems. Graph cuts based approaches to object extraction have also been shown to have interesting connections with earlier segmentation methods such as snakes, geodesic active contours, and level-sets. The segmentation energies optimized by graph cuts combine boundary regularization with region-based properties in the same fashion as Mumford-Shah style functionals. This paper presents motivation and detailed technical description of the basic combinatorial optimization framework for image segmentation via s/t graph cuts. After the general concept of using binary graph cut algorithms for object segmentation was first proposed and tested in [6], this idea was widely studied in computer vision and graphics communities. We provide links to a large number of known extensions based on iterative parameter re-estimation and learning, multi-scale or hierarchical approaches, narrow bands, and other techniques for demanding photo, video, and medical applications.

A fast implementation is possible via a new max-flow algorithm in BK:PAMI'04.

WHOLE PAPER: pdf file (802Kb)

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