The DOI matches its Crossref record; 26 of the 26 references it cites were found in a registry or an index.
Computing geodesics and minimal surfaces via graph cuts
Abstract
Geodesic active contours and graph cuts are two standard image segmentation techniques. We introduce a new segmentation method combining some of their benefits. Our main intuition is that any cut on a graph embedded in some continuous space can be interpreted as a contour (in 2D) or a surface (in 3D). We show how to build a grid graph and set its edge weights so that the cost of cuts is arbitrarily close to the length (area) of the corresponding contours (surfaces) for any anisotropic Riemannian metric. There are two interesting consequences of this technical result. First, graph cut algorithms can be used to find globally minimum geodesic contours (minimal surfaces in 3D) under arbitrary Riemannian metric for a given set of boundary conditions. Second, we show how to minimize metrication artifacts in existing graph-cut based methods in vision. Theoretically speaking, our work provides an interesting link between several branches of mathematics -differential geometry, integral geometry, and combinatorial optimization. The main technical problem is solved using Cauchy-Crofton formula from integral geometry.
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Cites
Kass, M., Witkin, A., & Terzopoulos, D. (1988) · International Journal of Computer Vision · doi:10.1007/bf00133570 · Cited by 17,070
Normalized cuts and image segmentation
Shi, J., & Malik, J. (2000) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.868688 · Cited by 15,502
Fast approximate energy minimization via graph cuts
Boykov, Y., Veksler, O., & Zabih, R. (2001) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.969114 · Cited by 6,988
Caselles, V., Kimmel, R., & Sapiro, G. (1997) · International Journal of Computer Vision · doi:10.1023/a:1007979827043 · Cited by 5,244
Level Set Methods and Dynamic Implicit Surfaces
Osher, S., & Fedkiw, R. (2003) · Applied Mathematical Sciences · doi:10.1007/b98879 · Cited by 4,951
An experimental comparison of min-cut/max- flow algorithms for energy minimization in vision
Boykov, Y., & Kolmogorov, V. (2004) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2004.60 · Cited by 4,577
Differential geometry of curves and surfaces
(2011) · Choice Reviews Online · doi:10.5860/choice.48-3330 · Cited by 3,706
Interactive graph cuts for optimal boundary & region segmentation of objects in N-D images
Boykov, Y. Y., & Jolly, M.-P. (2002) · Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001 · doi:10.1109/iccv.2001.937505 · Cited by 3,674
Level Set Methods and Fast Marching Methods
Sethian, J. A. (1999) · Medical Entomology and Zoology · Cited by 3,616
(2003) · Selected Papers of Alan J Hoffman · doi:10.1142/9789812796936_others05 · Cited by 2,465
Cited by
GrabCut: Interactive foreground extraction using iterated graph cuts
Rother, C., Kolmogorov, V., & Blake, A. (2004) · ACM Transactions on Graphics · doi:10.1145/1015706.1015720 · Cited by 5,703
An experimental comparison of min-cut/max- flow algorithms for energy minimization in vision
Boykov, Y., & Kolmogorov, V. (2004) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2004.60 · Cited by 4,577
What energy functions can be minimized via graph cuts?
Kolmogorov, V., & Zabih, R. (2004) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2004.1262177 · Cited by 3,127
Graph Cuts and Efficient N-D Image Segmentation
Boykov, Y., & Funka-Lea, G. (2006) · International Journal of Computer Vision · doi:10.1007/s11263-006-7934-5 · Cited by 1,910
A study on continuous max-flow and min-cut approaches
Yuan, J., Bae, E., & Tai, X.-C. (2010) · 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2010.5539903 · Cited by 237
Metadata
- Authors
- Boykov, & Kolmogorov
- Venue
- Proceedings Ninth IEEE International Conference on Computer Vision
- Publisher
- IEEE
- Published
- 2003
- Pages
- 26-33 vol.1
- OpenAlex
- W2105365768
- Cited by
- 555
- References
- 26
- FWCI
- 15.55
- Type
- conference paper
- Language
- en
- Open access
- closed
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