Fast global optimization of curvature

Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition

Volumn , Issue , 2010, Pages 3257-3264

  El Zehiry, Noha Youssry ^a   Grady, Leo ^a  

^a SIEMENS CORPORATE RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EXISTING METHOD; IMAGE MODELS; INPAINTING; MISSING DATA; NOISY DATA; OPTIMAL SOLUTIONS; RECENT PROGRESS; SUBOPTIMAL SOLUTION; TOTAL VARIATION;

COMPUTER VISION; GLOBAL OPTIMIZATION; IMAGE SEGMENTATION; OPTICAL FLOWS; OPTIMAL SYSTEMS; OPTIMIZATION; STEREO VISION;

CURVE FITTING;

EID: 77955995927     PISSN: 10636919     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CVPR.2010.5540057     Document Type: Conference Paper

References (31)

1. B. Appleton and H. Talbot. Globally optimal surfaces by continuous maximal flows. IEEE PAMI, 28(1):106-118, Jan. 2006.
2. E. Boros, P. L. Hammer, and X. Sun. Network fows and minimization of quadratic pseudo-boolean functions. Technical Report RRR 17-1991, RUTCOR, May 1991.
3. E. Boros, P. L. Hammer, and G. Tavares. Preprocessing of unconstrained quadratic binary optimization. Technical Report RRR 10-2006, RUTCOR, April 2006.
4. Y. Boykov and M.-P. Jolly. Interactive graph cuts for optimal boundary & region segmentation of objects in N-D images. In Proc. of ICCV, pages 105-112, 2001.
5. Y. Boykov and V. Kolmogorov. Computing geodesics and minimal surfaces via graph cuts. In Proc. of ICCV, volume 1, October 2003.
6. X. Bresson, S. Esedoglu, P. Vandergheynst, J. Thiran, and S. Osher. Fast global minimization of the active contour/snake model. JMIV, 28(2):151-167, 2007.
7. A. Bruckstein, A. Netravali, and Richardson. Epiconvergence of discrete elastica. Applicable Analysis, 79(1-2):137-171, 2001.
8. A. Chambolle. An algorithm for total variation minimization and applications. JMIV, 20(1-2):89-97, 2004.
9. T. F. Chan and L. A. Vese. Active contours without edges. IEEE Trans. Imag. Proc., 10(2):266-277, 2001.
10. G. Citti and A. Sarti. A cortical based model of perceptual completion in the roto-translation space. JMIV, 24(3):307-326, 2006.
11. J. Darbon and M. Sigelle. A fast and exact algorithm for total variation minimization. In IbPRIA (1), pages 351-359, 2005.
12. N. El-Zehiry, S. Xu, P. Sahoo, and A. Elmaghraby. Graph cut optimization for the Mumford Shah model. In VIIP, pages 182-187, 2007.
13. S. Esedoglu and J. Shen. Digital inpainting based on the mumfordshaheuler image model. European Journal of Applied Mathematics, 13(4):353-370, 2002.
14. T. Goldstein, X. Bresson, and S. Osher. Geometric applications of the split bregman method: Segmentation and surface reconstruction. Technical Report 09-06, UCLA, 2009.
15. L. Grady and C. Alvino. The piecewise smooth Mumford-Shah functional on an arbitrary graph. IEEE Trans. on Image Proc., 18(11):2547-2561, Nov. 2009.
16. P. L. Hammer, P. Hansen, and B. Simeone. Roof duality, complementation and persistency in quadratic 0 1 optimization. Mathematical Programming, 28(2):121-155, 1984.
17. I. H. Jermyn and H. Ishikawa. Globally optimal regions and boundaries as minimum ratio weight cycles. IEEE PAMI, pages 1075-1088, 2001.
18. V. Kolmogorov and C. Rother. Minimizing nonsubmodular functions with graph cuts-a review. IEEE PAMI, 29(7):1274-1279, 2007.
19. V. Kolmogorov and R. Zabih. What energy functions can be minimized via graph cuts? IEEE PAMI, 26(2):147-159, 2004.
20. S. Masnou and J.-M. Morel. Level lines based. In ICIP (3), pages 259-263, 1998.
21. M. Meyer, M. Desbrun, P. Schröder, and A. H. Barr. Discrete differential-geometry operators for triangulated 2-manifolds. In Visualization and Mathematics III, pages 35-57. Springer-Verlag, Heidelberg, 2003.
22. D. Mumford. Elastica and computer vision. Algebriac Geometry and Its Applications, pages 491-506, 1994.
23. D. Mumford and J. Shah. Optimal approximations by piecewise smooth functions and associated variational problems. Comm. on Pure and App. Math., 42(5):577-685, 1989.
24. P. Parent and S. W. Zucker. Trace inference, curvature consistency, and curve detection. IEEE PAMI, 11(8):823-839, 1989.
25. C. Rother, V. Kolmogorov, V. S. Lempitsky, and M. Szummer. Optimizing binary MRFs via extended roof duality. In CVPR, 2007.
26. L. Rudin, S. Osher, and E. Fatemi. Nonlinear total variation based noise removal algorithms. Phy. D, 60:259-268, 1992.
27. T. Schoenemann and D. Cremers. Introducing curvature into globally optimal image segmentation: Minimum ratio cycles on product graphs. In ICCV, pages 1-6, 2007.
28. T. Schoenemann, F. Kahl, and D. Cremers. Curvature regularity for region-based image segmentation and inpainting: A linear programming relaxation. In ICCV, Kyoto, Japan, 2009.
29. J. Shen, S. H. Kang, and T. F. Chan. Euler's elastica and curvature-based inpainting. SIAM Journal of Applied Mathematics, 63(2):564-592, 2003.
30. M. Unger, T. Pock, W. Trobin, D. Cremers, and H. Bischof. TVSeg - Interactive total variation based image segmentation. In BMVC, 2008.
31. W. Zhu and T. Chan. A variational model for capturing illusory contours using curvature. J. Math. Imaging Vis., 27(1):29-40, 2007.