Abstract
We address the problem of segmenting an image into a previously unknown number of segments from the perspective of graph partitioning. Specifically, we consider minimum multicuts of superpixel affinity graphs in which all affinities between non-adjacent superpixels are negative. We propose a relaxation by Lagrangian decomposition and a constrained set of re-parameterizations for which we can optimize exactly and efficiently. Our contribution is to show how the planarity of the adjacency graph can be exploited if the affinity graph is non-planar. We demonstrate the effectiveness of this approach in user-assisted image segmentation and show that the solution of the relaxed problem is fast and the relaxation is tight in practice.
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References
Andres, B.: https://github.com/bjoern-andres/graph
Andres, B., Kappes, J.H., Beier, T., Köthe, U., Hamprecht, F.A.: Probabilistic image segmentation with closedness constraints. In: ICCV (2011)
Andres, B., Kroeger, T., Briggman, K.L., Denk, W., Korogod, N., Knott, G., Koethe, U., Hamprecht, F.A.: Globally optimal closed-surface segmentation for connectomics. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part III. LNCS, vol. 7574, pp. 778–791. Springer, Heidelberg (2012)
Arbelaez, P., Maire, M., Fowlkes, C., Malik, J.: Contour detection and hierarchical image segmentation. TPAMI 33(5), 898–916 (2011)
Bachrach, Y., Kohli, P., Kolmogorov, V., Zadimoghaddam, M.: Optimal coalition structures in graph games. arXiv ePrint (2011)
Bagon, S., Galun, M.: Large scale correlation clustering optimization. arXiv ePrint, abs/1112.2903 (2011)
Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Machine Learning 56, 89–113 (2004)
Chopra, S., Rao, M.R.: The partition problem. Math. Program. 59, 87–115 (1993)
Kappes, J.H., Speth, M., Andres, B., Reinelt, G., Schnörr, C.: Globally optimal image partitioning by multicuts. In: Boykov, Y., Kahl, F., Lempitsky, V., Schmidt, F.R. (eds.) EMMCVPR 2011. LNCS, vol. 6819, pp. 31–44. Springer, Heidelberg (2011)
Kim, S., Nowozin, S., Kohli, P., Yoo, C.D.: Higher-order correlation clustering for image segmentation. In: NIPS (2011)
Kolmogorov, V.: Blossom V: a new implementation of a minimum cost perfect matching algorithm. Mathematical Programming Computation 1(1), 43–67 (2009)
Nowozin, S., Jegelka, S.: Solution stability in linear programming relaxations: graph partitioning and unsupervised learning. In: ICML, pp. 769–776 (2009)
Nowozin, S., Lampert, C.H.: Global interactions in random field models: A potential function ensuring connectedness. SIAM J. Img. Sci. 3(4), 1048–1074 (2010)
Shih, W.-K., Wu, S., Kuo, Y.S.: Unifying maximum cut and minimum cut of a planar graph. IEEE Trans. Comput. 39(5), 694–697 (1990)
Vitaladevuni, S.N.P., Basri, R.: Co-clustering of image segments using convex optimization applied to EM neuronal reconstruction. In: CVPR (2010)
Yarkony, J.: MAP inference in Planar Markov Random Fields with Applications to Computer Vision. PhD thesis, University of California, Irvine (2012)
Yarkony, J., Ihler, A., Fowlkes, C.C.: Fast planar correlation clustering for image segmentation. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part VI. LNCS, vol. 7577, pp. 568–581. Springer, Heidelberg (2012)
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Andres, B. et al. (2013). Segmenting Planar Superpixel Adjacency Graphs w.r.t. Non-planar Superpixel Affinity Graphs. In: Heyden, A., Kahl, F., Olsson, C., Oskarsson, M., Tai, XC. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2013. Lecture Notes in Computer Science, vol 8081. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40395-8_20
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DOI: https://doi.org/10.1007/978-3-642-40395-8_20
Publisher Name: Springer, Berlin, Heidelberg
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