New algorithms for convex cost tension problem with application to computer vision

Discrete Optimization

Volumn 6, Issue 4, 2009, Pages 378-393

  Kolmogorov, Vladimir ^a   Shioura, Akiyoshi ^b  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b TOHOKU UNIVERSITY   (Japan)

Author keywords

Discrete convex function; Minimum cost flow; Minimum cost tension; Submodular function

Indexed keywords

COMPUTER VISION PROBLEMS; CONVEX COST; DISCRETE CONVEX FUNCTION; MINIMUM COST FLOW; MINIMUM COST TENSION; MINIMUM CUT; OPTIMAL SOLUTIONS; PANORAMIC IMAGES; PRIMAL ALGORITHM; PRIMAL DUAL ALGORITHMS; SUBMODULAR FUNCTION; TIME COMPLEXITY;

ALGORITHMS; COMPUTATION THEORY; COMPUTER APPLICATIONS; COMPUTER VISION; COST ACCOUNTING; EDGE DETECTION; MATHEMATICAL OPERATORS;

COSTS;

EID: 68449099927     PISSN: 15725286     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.disopt.2009.04.006     Document Type: Article

References (37)

1. Ahuja R.K., Hochbaum D.S., and Orlin J.B. Solving the convex cost integer dual network flow problem. Manage. Sci. 49 (2003) 950-964
2. Iri M. Network Flow, Transportation and Scheduling - Theory and Algorithms (1969), Academic Press, New York, NY
3. Murota K. On steepest descent algorithms for discrete convex functions. SIAM J. Optim 14 (2003) 699-707
4. Rockafellar R.T. Network Flows and Monotropic Optimization (1984), Wiley, New York, NY
5. Boykov Y., Veksler O., and Zabih R. Fast approximate energy minimization via graph cuts. IEEE Trans. Pattern Anal. Mach. Intell. 23 (2001) 1222-1239
6. Chambolle A. Total variation minimization and a class of binary MRF models. 5th International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition. LNCS vol. 3757 (2005), Springer, Berlin 136-152
7. Darbon J., and Sigelle M. A fast and exact algorithm for total variation minimization. Proc. of Pattern Recognition and Image Analysis, 2nd Iberian Conf. IbPRIA. LNCS vol. 3533 (2005), Springer, Berlin 351-359
8. Hochbaum D.S. An efficient algorithm for image segmentation, Markov random fields and related problems. J. ACM 48 (2001) 686-701
9. Ishikawa H. Exact optimization for Markov random fields with convex priors. IEEE Trans. Pattern Anal. Mach. Intell. 25 (2003) 1333-1336
10. Levin A., Zomet A., Peleg S., and Weiss Y. Seamless image stitching in the gradient domain. Proc. of 8th European Conf. on Computer Vision. LNCS vol. 3024 (2004), Springer, Berlin 377-389
11. Zalesky B. Network flow optimization for restoration of images. J. Appl. Math. 2 (2002) 199-218
12. B. Zalesky, Fast algorithms of Bayesian segmentation of images, Preprint, 2002. arXiv:math/0206184v2
13. B. Zalesky, Efficient determination of Gibbs estimators with submodular energy functions, Preprint, 2003. arXiv:math/0304041v1
14. Zomet A., Levin A., Peleg S., and Weiss Y. Seamless image stitching by minimizing false edges. IEEE Trans. Image Process. 15 (2006) 969-977
15. Ahuja R.K., Hochbaum D.S., and Orlin J.B. A cut based algorithm for the convex dual of the minimum cost network flow problem. Algorithmica 39 (2004) 189-208
16. Karzanov A.B., and McCormick S.T. Polynomial methods for separable convex optimization in unimodular linear spaces with applications. SIAM J. Comput. 4 (1997) 1245-1275
17. Ford L.R., and Fulkerson D.R. A primal-dual algorithm for the capacitated Hitchcock problem. Naval Res. Logist. Quart. 4 (1957) 47-54
18. Ford L.R., and Fulkerson D.R. Flows in Networks (1962), Princeton Univ. Press, Princeton, NJ
19. Murota K. Algorithms in discrete convex analysis. IEICE Trans. Inform. Syst. E83-D (2000) 344-352
20. Murota K. Discrete Convex Analysis (2003), Society for Industrial and Applied Mathematics, Philadelphia, PA
21. Bioucas-Dias J., and Valadão G. Phase unwrapping via graph cuts. Proc. of Pattern Recognition and Image Analysis, 2nd Iberian Conf. IbPRIA. LNCS vol. 3533 (2005), Springer, Berlin 360-367
22. Ahuja R.K., Magnanti T.L., and Orlin J.B. Network Flows: Theory, Algorithms, and Applications (1993), Prentice Hall, Englewood, NJ
23. Minoux M. A polynomial algorithm for minimum quadratic cost flow problems. European J. Oper. Res. 18 (1984) 377-387
24. Boykov Y., and Kolmogorov V. An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision. IEEE Trans. Pattern Anal. Mach. Intell. 26 (2004) 1124-1137
25. Kleinberg J., and Tardos E. Approximation algorithms for classification problems with pairwise relationships: Metric labeling and Markov random fields. Proc. of 40th Annual Symp. on Foundations of Computer Science (1999), FOCS IEEE Computer Society, Washington DC 14-23
26. Komodakis N., and Tziritas G. A new framework for approximate labeling via graph cuts. Proc. of 10th IEEE Int. Conf. on Computer Vision (2005), IEEE Computer Society, Washington DC 1018-1025
27. O. Veksler, Efficient graph-based energy minimization methods in computer vision, Ph.D. Thesis, Cornell University, 1999
28. Geman S., and Geman D. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6 (1984) 721-741
29. Boros E., and Hammer P.L. Pseudo-boolean optimization. Discrete Appl. Math. 123 (2002) 155-225
30. V. Kolmogorov, Primal-dual algorithm for convex Markov random fields, Technical Report MSR-TR-2005-117, Microsoft Research, 2005
31. J. Darbon, Composants logiciels et algorithmes de minimisation exacte d'énergies dédiées au traitement des images, Ph.D. Thesis, Ecole Nationale Supérieure des Télécommunications, October 2005 (in French)
32. Bioucas-Dias J., and Valadão G. Phase unwrapping via graph cuts. IEEE Trans. Image Process. 16 (2007) 698-709
33. Fujishige A., and Murota K. Notes on L-/M-convex functions and the separation theorems. Math. Program. 88 (2000) 129-146
34. Murota K. Discrete convex analysis. Math. Program. 83 (1998) 313-371
35. Favati P., and Tardella F. Convexity in nonlinear integer programming. Ric. Oper. 53 (1990) 3-44
36. Orlin J.B. A faster strongly polynomial time algorithm for submodular function minimization. Math. Program. 118 (2009) 237-251
37. Goldberg A.V. An efficient implementation of a scaling minimum-cost flow algorithm. J. Algorithms 22 (1997) 1-29