Generalized roof duality

Discrete Applied Mathematics

Volumn 160, Issue 16-17, 2012, Pages 2419-2434

  Kahl, Fredrik ^a   Strandmark, Petter ^a  

^a LUND UNIVERSITY   (Sweden)

Author keywords

Computer vision; Higher order; MRF; Roof duality

Indexed keywords

AUXILIARY VARIABLES; BINARY OPTIMIZATION; COMBINATORIAL PROBLEM; DUAL BOUND; DUALITY TECHNIQUES; HIGHER-ORDER; HIGHER-ORDER PROBLEMS; LOWER BOUNDS; MRF; OBJECTIVE FUNCTIONS; OPTIMAL VALUES; OPTIMIZATION PROBLEMS; PSEUDO-BOOLEAN FUNCTION; STATE OF THE ART; SUBMODULAR; SUBMODULAR FUNCTIONS;

BOOLEAN FUNCTIONS; COMPUTER VISION; OPTIMIZATION;

ROOFS;

EID: 84865103957     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2012.06.009     Document Type: Article

References (36)

1. A. Billionet, and M. Minoux Maximizing a supermodular pseudo-boolean function: a polynomial algorithm for cubic functions Discrete Appl. Math. 12 1985 1 11 (Pubitemid 15542397)
2. A. Billionnet, and A. Sutter Persistency in quadratic 01 optimization Math. Program. 54 13 1992 115 119
3. E. Boros, and P.L. Hammer Pseudo-boolean optimization Discrete Appl. Math. 123 2002 155 225
4. E. Boros, P.L. Hammer, R. Sun, and G. Tavares A max-flow approach to improved lower bounds for quadratic unconstrained binary optimization (QUBO) Discrete Optim. 5 2 2008 501 529 (Pubitemid 351443144)
5. Y. Boykov, O. Veksler, and R. Zabih Fast approximate energy minimization via graph cuts IEEE Trans. Pattern Anal. Mach. Intell. 23 11 2001 1222 1239 (Pubitemid 33137959)
6. Y. Crama Recognition problems for special classes of polynomials in 01 variables Math. Program. 44 13 1989 139 155
7. D. Cremers, L. Grady, Statistical priors for efficient combinatorial optimization via graph cuts, in: European Conf. Computer Vision, Graz, Austria, 2006.
8. A. Fix, A. Grubner, E. Boros, R. Zabih, A graph cut algorithm for higher-order Markov random fields, in: Int. Conf. Computer Vision, Barcelona, Spain, 2011.
9. D. Freedman, P. Drineas, Energy minimization via graph cuts: settling what is possible, in: Conf. Computer Vision and Pattern Recognition, San Diego, USA, 2005.
10. S. Fujishige, and S. Iwata Bisubmodular function minimization SIAM J. Discrete Math. 19 4 2006 1065 1073 (Pubitemid 44775303)
11. A.C. Gallagher, D. Batra, D. Parikh, Inference for order reduction in Markov random fields, in: Conf. Computer Vision and Pattern Recognition, Colorado Springs, USA, 2011.
12. F. Glover, B. Alidaee, C. Rego, and G. Kochenberger One-pass heuristics for large-scale unconstrained binary quadratic problems European J. Oper. Res. 137 2 2002 272 287 (Pubitemid 34000339)
13. P.L. Hammer, P. Hansen, and B. Simeone Roof duality, complementation and persistency in quadratic 01 optimization Math. Program. 28 2 1984 121 155 (Pubitemid 14569633)
14. H.H. Hoos, and T. Sttzle SATLIB: an online resource for research on SAT SAT 2000 2000 IOS Press 283 292
15. H. Ishikawa Transformation of general binary MRF minimization to the first order case IEEE Trans. Pattern Anal. Mach. Intell. 33 6 2011 1234 1249
16. F. Kahl, P. Strandmark, Generalized roof duality for pseudo-boolean functions, in: Int. Conf. Computer Vision, Barcelona, Spain, 2011.
17. P. Kohli, M.P. Kumar, and P.H.S. Torr P 3 & beyond: move making algorithms for solving higher order functions IEEE Trans. Pattern Anal. Mach. Intell. 31 9 2009 1645 1656
18. V. Kolmogorov Generalized roof duality and bisubmodular functions Discrete Appl. Math. 160 45 2012 416 426
19. V. Kolmogorov, and C. Rother Minimizing nonsubmodular functions with graph cutsa review IEEE Trans. Pattern Anal. Mach. Intell. 29 7 2007 1274 1279 (Pubitemid 46838518)
20. N. Komodakis, N. Paragios, Beyond pairwise energies: efficient optimization for higher-order MRFs, in: Conf. Computer Vision and Pattern Recognition, Miami, USA, 2009.
21. L. Ladicky, C. Russell, P. Kohli, P.H.S. Torr, Graph cut based inference with co-occurrence statistics, in: European Conf. Computer Vision, Crete, Greece, 2010.
22. X. Lan, S. Roth, D.P. Huttenlocher, M.J. Black, Efficient belief propagation with learned higher-order Markov random fields, in: European Conf. Computer Vision, Graz, Austria, 2006.
23. V. Lempitsky, C. Rother, S. Roth, and A. Blake Fusion moves for Markov random field optimization IEEE Trans. Pattern Anal. Mach. Intell. 32 8 2010 1392 1405
24. L. Lovsz Submodular functions and convexity Mathematical Programming: The State of the Art 1983 235 257
25. S.H. Lu, and A.C. Williams Roof duality for polynomial 01 optimization Math. Program. 37 3 1987 357 360
26. S. Nowozin, and C.H. Lampert Global interactions in random field models: a potential function ensuring connectedness SIAM J. Imaging Sciences 3 4 2010 1048 1074
27. S.D. Promislow, and V.R. Young Supermodular functions on finite lattices Order 22 4 2005 389 413 (Pubitemid 43473703)
28. C. Rother, P. Kohli, W. Feng, J. Jia, Minimizing sparse higher order energy functions of discrete variables, in: Conf. Computer Vision and Pattern Recognition, Miami, USA, 2009.
29. T. Schoenemann, F. Kahl, D. Cremers, Curvature regularity for region-based image segmentation and inpainting: a linear programming relaxation, in: Int. Conf. Computer Vision, Kyoto, Japan, 2009.
30. P. Strandmark, and F. Kahl Curvature regularization for curves and surfaces in a global optimization framework Energy Minimization Methods in Computer Vision and Pattern Recognition Lecture Notes in Computer Science vol. 6819 2011 Springer
31. P. Strandmark, F. Kahl, Parallel and distributed graph cuts by dual decomposition, in: Conf. Computer Vision and Pattern Recognition, San Francisco, USA, 2010.
32. T. Werner, High-arity interactions, polyhedral relaxations, and cutting plane algorithm for MAP-MRF, in: Conf. Computer Vision and Pattern Recognition, Anchorage, USA, 2008.
33. O.J. Woodford, P.H.S. Torr, I.D. Reid, and A.W. Fitzgibbon Global stereo reconstruction under second-order smoothness priors IEEE Trans. Pattern Anal. Mach. Intell. 31 12 2009 2115 2128
34. S. Zivný, D.A. Cohen, and P.G. Jeavons The expressive power of binary submodular functions Discrete Appl. Math. 157 15 2009 3347 3358
35. S. Zivný, and P.G. Jeavons Classes of submodular constraints expressible by graph cuts Constraints 15 3 2010 430 452
36. S. Zivný, P.G. Jeavons, Which submodular functions are expressible using binary submodular functions? Technical Report CS-RR-08-08, Oxford University Computing Laboratory, 2008.