Abstract
We describe a new optimization scheme for finding high-quality clusterings in planar graphs that uses weighted perfect matching as a subroutine. Our method provides lower-bounds on the energy of the optimal correlation clustering that are typically fast to compute and tight in practice. We demonstrate our algorithm on the problem of image segmentation where this approach outperforms existing global optimization techniques in minimizing the objective and is competitive with the state of the art in producing high-quality segmentations.
Chapter PDF
Similar content being viewed by others
Keywords
- Image Segmentation
- Planar Graph
- Integer Linear Programming
- Markov Random Field
- Linear Programming Relaxation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Borenstein, E., Ullman, S.: Combined top-down/bottom-up segmentation. TPAMI 30 (2008)
Winn, J., Shotton, J.: The layout consistent random field for recognizing and segmenting partially occluded objects. In: CVPR (2006)
Yang, Y., Hallman, S., Ramanan, D., Fowlkes, C.: Layered object models for image segmentation. TPAMI 34, 1731–1743 (2011)
Gould, S., Gao, T., Koller, D.: Region-based segmentation and object detection. In: NIPS (2009)
Ladický, L., Sturgess, P., Alahari, K., Russell, C., Torr, P.H.S.: What, Where and How Many? Combining Object Detectors and CRFs. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part IV. LNCS, vol. 6314, pp. 424–437. Springer, Heidelberg (2010)
Shi, J., Malik, J.: Normalized cuts and image segmentation. TPAMI 22, 888–905 (2000)
Wang, S., Kubota, T., Siskind, J.M., Wang, J.: Salient closed boundary extraction with ratio contour. PAMI (2005)
Zhu, Q., Song, G., Shi, J.: Untangling cycles for contour grouping. In: ICCV (2007)
Sharon, E., Galun, M., Sharon, D., Basri, R., Brandt, A.: Hierarchy and adaptivity in segmenting visual scenes. Nature 442, 810–813 (2006)
Cour, T., Benezit, F., Shi, J.: Spectral segmentation with multiscale graph decomposition. In: CVPR (2005)
Taskar, B.: Learning Structured Prediction Models: A Large Margin Approach. Stanford University (2004)
Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Machine Learning 56, 89–113 (2004)
Demaine, E., Emanuel, D., Fiat, A., Immorlica, N.: Correlation clustering in general weighted graphs. Theoretical Computer Science 361, 172–187 (2006)
Dahlhaus, E., Johnson, D., Papadimitriou, C., Seymour, P., Yannakakis, M.: The complexity of multiterminal cuts. SIAM J. Computing 4, 864–894 (1994)
Bachrach, Y., Kohli, P., Kolmogorov, V., Zadimoghaddam, M.: Optimal coalition structures in graph games. arXiv:1108.5248v1 (2011)
Andres, B., Kappes, J., Beier, T., Koethe, U., Hamprecht, F.: Probabilistic image segmentaiton with closedness constraints. In: ICCV (2011)
Kim, S., Nowozin, S., Kohli, P., Yoo, C.: Higher-order correlation clustering for image segmentation. In: NIPS (2011)
Appel, K., Haken, W.: Every Planar Map is Four-Colorable. American Mathematical Society (1989)
Wainwright, M.J., Jaakkola, T., Willsky, A.S.: MAP estimation via agreement on (hyper)trees: message-passing and linear programming approaches. IEEE Trans. Inform. Theory 51, 3697–3717 (2005)
Kolmogorov, V.: Convergent tree-reweighted message passing for energy minimization. IEEE Trans. Pattern Anal. Machine Intell. 28, 1568–1583 (2006)
Kasteleyn, P.: Graph theory and crystal physics. In: Harary, F. (ed.) Graph Theory and Theoretical Physics, pp. 43–110 (1967)
Fisher, M.: On the dimer solution of planar Ising models 7, 1776–1781 (1966)
Globerson, A., Jaakkola, T.: Approximate inference using planar graph decomposition. In: NIPS (2007)
Schraudolph, N., Kamenetsky, D.: Efficient exact inference in planar Ising models. In: NIPS (2009)
Schraudolph, N.: Polynomial-time exact inference in np-hard binary MRFs via reweighted perfect matching. In: AISTATS (2010)
Batra, D., Gallagher, A., Parikh, D., Chen, T.: Beyond trees: MRF inference via outer-planar decomposition. In: CVPR (2010)
Yarkony, J., Ihler, A., Fowlkes, C.: Planar cycle covering graphs. In: UAI (2011)
Komodakis, N., Paragios, N., Tziritas, G.: MRF optimization via dual decomposition: Message-passing revisited. In: ICCV (2007)
Yarkony, J.: Planarity Matters: MAP inference in Planar Markov Random Fields with Applications to Computer Vision. University of California, Irvine (2012)
Deza, M., Laurent, M.: Geometry of cuts and metrics. Springer (1997)
Barahona, F.: The max cut problem in graphs not contractible to k 5. Operations Research Letters 2, 107–111 (1983)
Martin, D., Fowlkes, C., Tal, D., Malik, J.: A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: ICCV (2001)
Arbelaez, P., Maire, M., Fowlkes, C., Malik, J.: Contour detection and hierarchical image segmentation. TPAMI 33, 898–916 (2011)
Kolmogorov, V.: Blossom V: A new implementation of a minimum cost perfect matching algorithm. Mathematical Programming Computation 1(1), 43–67 (2009)
Schraudolph, N., Kamenetsky, D.: Efficient exact inference in planar Ising models. Technical Report 0810.4401 (2008)
Sontag, D., Meltzer, T., Globerson, A., Weiss, Y., Jaakkola, T.: Tightening LP relaxations for MAP using message passing. In: UAI (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Yarkony, J., Ihler, A., Fowlkes, C.C. (2012). Fast Planar Correlation Clustering for Image Segmentation. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds) Computer Vision – ECCV 2012. ECCV 2012. Lecture Notes in Computer Science, vol 7577. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33783-3_41
Download citation
DOI: https://doi.org/10.1007/978-3-642-33783-3_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33782-6
Online ISBN: 978-3-642-33783-3
eBook Packages: Computer ScienceComputer Science (R0)