Abstract
We propose a novel method to obtain a part of an optimal non-relaxed integral solution for energy minimization problems with Potts interactions, known also as the minimal partition problem. The method empirically outperforms previous approaches likeMQPBO and Kovtun’s method in most of our test instances and especially in hard ones. As a starting point our approach uses the solution of a commonly accepted convex relaxation of the problem. This solution is then iteratively pruned until our criterion for partial optimality is satisfied. Due to its generality our method can employ any solver for the considered relaxed problem.
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References
Brainweb: Simulated brain database, http://brainweb.bic.mni.mcgill.ca/brainweb/
OpenGM inference library, http://hci.iwr.uni-heidelberg.de/opengm2/
Alahari, K., Kohli, P., Torr, P.H.S.: Reduce, reuse & recycle: Efficiently solving multi-label MRFs. In: CVPR (2008)
Alahari, K., Kohli, P., Torr, P.H.S.: Dynamic hybrid algorithms for MAP inference in discrete MRFs. PAMI 32(10), 1846–1857 (2010)
Boros, E., Hammer, P.L.: Pseudo-Boolean optimization. Discrete Applied Mathematics 123(1-3), 155–225 (2002)
Boykov, Y., Kolmogorov, V.: Computing geodesics and minimal surfaces via graph cuts. In: ICCV, pp. 26–33. IEEE Computer Society (2003)
Chambolle, A., Cremers, D., Pock, T.: A convex approach for computing minimal partitions. Technical report, Centre des Mathematiques Appliquees, Ecole Polytechnique, Palaiseau, Paris, France (2008)
Chambolle, A., Pock, T.: A first-order primal-dual algorithm for convex problems with applications to imaging. Journal of Mathematical Imaging and Vision 40(1), 120–145 (2011)
Hammer, P.L., Hansen, P., Simeone, B.: Roof duality, complementation and persistency in quadratic 0-1 optimization. Math. Programming 28, 121–155 (1984)
Kahl, F., Strandmark, P.: Generalized roof duality. Discrete Applied Mathematics 160(16-17), 2419–2434 (2012)
Kappes, J.H., Andres, B., Hamprecht, F.A., Schnörr, C., Nowozin, S., Batra, D., Kim, S., Kausler, B.X., Lellmann, J., Komodakis, N., Rother, C.: A comparative study of modern inference techniques for discrete energy minimization problem. In: CVPR (2013)
Kleinberg, J., Tardos, É.: Approximation algorithms for classification problems with pairwise relationships: metric labeling and Markov random fields. J. ACM 49(5), 616–639 (2002)
Kohli, P., Shekhovtsov, A., Rother, C., Kolmogorov, V., Torr, P.: On partial optimality in multi-label MRFs. In: ICML, pp. 480–487 (2008)
Kovtun, I.: Partial optimal labeling search for a NP-hard subclass of (max,+) problems. In: Michaelis, B., Krell, G. (eds.) DAGM 2003. LNCS, vol. 2781, pp. 402–409. Springer, Heidelberg (2003)
Lellmann, J., Schnörr, C.: Continuous multiclass labeling approaches and algorithms. SIAM J. Imag. Sci. 4(4), 1049–1096 (2011)
Nemhauser, G.L., Trotter, L.E.: Vertex packings: Structural properties and algorithms. Mathematical Programming 8, 232–248 (1975), doi:10.1007/BF01580444
Rother, C., Kolmogorov, V., Lempitsky, V.S., Szummer, M.: Optimizing binary MRFs via extended roof duality. In: CVPR (2007)
Shekhovtsov, A., Kolmogorov, V., Kohli, P., Hlavac, V., Rother, C., Torr, P.: LP-relaxation of binarized energy minimization. Research Report CTU–CMP–2007–27, Czech Technical University (2008)
Sontag, D.: Approximate Inference in Graphical Models using LP Relaxations. PhD thesis, Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science (2010)
Windheuser, T., Ishikawa, H., Cremers, D.: Generalized Roof Duality for Multi-Label Optimization: Optimal Lower Bounds and Persistency. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part VI. LNCS, vol. 7577, pp. 400–413. Springer, Heidelberg (2012)
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Swoboda, P., Savchynskyy, B., Kappes, J., Schnörr, C. (2013). Partial Optimality via Iterative Pruning for the Potts Model. In: Kuijper, A., Bredies, K., Pock, T., Bischof, H. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2013. Lecture Notes in Computer Science, vol 7893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38267-3_40
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DOI: https://doi.org/10.1007/978-3-642-38267-3_40
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