Abstract
In this work we show, that for each permuted submodular MinSum problem (Energy Minimization Task) the corresponding submodular MinSum problem can be found in polynomial time. It follows, that permuted submodular MinSum problems are exactly solvable by transforming them into corresponding submodular tasks followed by applying standart approaches (e.g. using MinCut-MaxFlow based techniques).
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References
Besag, J.: On the statistical analysis of dirty pictures (with discussion). Journal of the Royal Statistical Society, Series B 48(3), 259–302 (1986)
Boykov, Y., Veksler, O., Zabih, R.: Fast approximate energy minimization via graph cuts, ICCV, pp. 377–384 (1999)
Flach, B.: Strukturelle Bilderkennung: Habilitationsschrift, Dresden University of Technology, in German (2003)
Flach, B., Schlesinger, D., Kask, E., Skulisch, A.: Unifying registration and segmentation for multi-sensor images. In: Van Gool, L. (ed.) Pattern Recognition. LNCS, vol. 2449, pp. 190–197. Springer, Heidelberg (2002)
Greig, D.M., Porteous, B.T., Seheult, A.H.: Exact maximum a posteriori estimation for binary images. J. R. Statist. Soc. 51(2), 271–279 (1989)
Ishikawa, H.: Exact optimization for markov random fields with convex priors. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(10), 1333–1336 (2003)
Ishikawa, H., Geiger, D.: Segmentation by grouping junctions. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition (1998)
Keuchel, J., Schnörr, C., Schellewald, C., Cremers, D.: Binary partitioning, perceptual grouping, and restoration with semidefinite programming. IEEE Transactions on Pattern Analysis and Machine Intelligence 25(11), 1364–1379 (2003)
Kolmogorov, V.: Convergent tree-reweighted message passing for energy minimization. IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI) 28(10), 1568–1583 (2006)
Kolmogorov, V., Zabih, R.: Computing visual correspondence with occlusions via graph cuts. In: International Conference on Computer Vision, pp. 508–515 (2001)
Kolmogorov, V., Zabih, R.: What energy functions can be minimized via graph cuts? In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2352, pp. 65–81. Springer, Heidelberg (2002)
Kovtun, I.: Texture segmentation of images on the basis of markov random fields, Tech. report, TUD-FI03 (May 2003)
Schlesinger, M.I., Hlavác, V.: Ten lectures on statistical and structural pattern recognition. Kluwer Academic Publishers, Dordrecht (2002)
Schlesinger, M.I., Giginyak, V.V.: Solution to structural recognition (max,+)-problems by their equivalent transformations, Control Systems and Machines, Naukova Dumka, Kiev, no. 1,2, in Russian (2007)
Schlesinger, D.: Gibbs probability distributions for stereo reconstruction. In: Michaelis, B., Krell, G. (eds.) Pattern Recognition. LNCS, vol. 2781, pp. 394–401. Springer, Heidelberg (2003)
Schlesinger, D., Flach, B.: Transforming an arbitrary minsum problem into a binary one, Tech. report, Dresden University of Technology, TUD-FI06-01 (April 2005), http://www.bv.inf.tu-dresden.de/~ds24/tr_kto2.pdf
Schlesinger, M.I., Flach, B.: Some solvable subclasses of structural recognition problems. In: Svoboda, T. (ed.) Czech Pattern Recognition Workshop 2000, pp. 55–62 (2000)
Shlezinger, D.: Strukturelle Ansätze für die Stereorekonstruktion, Ph.D. thesis, Dresden University of Technology, in German (2005), http://nbn-resolving.de/
Werner, T.: A linear programming approach to max-sum problem: A review, Tech. Report CTU–CMP–2005–25, Center for Machine Perception, K13133 FEE Czech Technical University (December 2005)
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Schlesinger, D. (2007). Exact Solution of Permuted Submodular MinSum Problems. In: Yuille, A.L., Zhu, SC., Cremers, D., Wang, Y. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2007. Lecture Notes in Computer Science, vol 4679. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74198-5_3
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DOI: https://doi.org/10.1007/978-3-540-74198-5_3
Publisher Name: Springer, Berlin, Heidelberg
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