Abstract
Graph matching has been a fundamental problem in computer vision and pattern recognition, for its practical flexibility as well as NP hardness challenge. Though the matching between two graphs and among multiple graphs have been intensively studied in literature, the online setting for incremental matching of a stream of graphs has been rarely considered. In this paper, we treat the graphs as graphs on a super-graph, and propose a novel breadth first search based method for expanding the neighborhood on the super-graph for a new coming graph, such that the matching with the new graph can be efficiently performed within the constructed neighborhood. Then depth first search is performed to update the overall pairwise matchings. Moreover, we show our approach can also be readily used in the batch mode setting, by adaptively determining the order of coming graph batch for matching, still under the neighborhood expansion based incremental matching framework. Experiments on both online and offline matching of graph collections show our approach’s state-of-the-art accuracy and efficiency.
Keywords
Work was partly supported by National Key Research and Development Program of China 2018AAA0100704, NSFC (61972250, U19B2035), and SJTU Global Strategic Partnership Fund (2020 SJTU-CORNELL).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
We assume graphs are of equal size in this paper, which can be obtained by adding dummy nodes if needed as widely done in literature [6].
References
Bunke, H.: Graph matching: theoretical foundations, algorithms, and applications. In: Vision Interface (2000)
Caetano, T., McAuley, J., Cheng, L., Le, Q., Smola, A.J.: Learning graph matching. TPAMI 31(6), 1048–1058 (2009)
Chen, Y., Guibas, L., Huang, Q.: Near-optimal joint object matching via convex relaxation. In: ICML (2014)
Chertok, M., Keller, Y.: Efficient high order matching. TPAMI 32, 2205–2215 (2010)
Cho, M., Alahari, K., Ponce, J.: Learning graphs to match. In: ICCV (2013)
Cho, M., Lee, J., Lee, K.M.: Reweighted random walks for graph matching. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010. LNCS, vol. 6315, pp. 492–505. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15555-0_36
Conte, D., Foggia, P., Sansone, C., Vento, M.: Thirty years of graph matching in pattern recognition. IJPRAI 18, 265–298 (2004)
Duchenne, O., Bach, F., Kweon, I., Ponce, J.: A tensor-based algorithm for high-order graph matching. TPAMI 33, 2383–2395 (2011)
Egozi, A., Keller, Y., Guterman, H.: A probabilistic approach to spectral graph matching. TPAMI 35, 18–27 (2013)
Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM 24, 381–395 (1981)
Foggia, P., Percannella, G., Vento, M.: Graph matching and learning in pattern recognition in the last 10 years. IJPRAI 33(1), 1450001 (2014)
Garey, M.R., Johnson, D.S.: Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, New York (1990)
Gold, S., Rangarajan, A.: A graduated assignment algorithm for graph matching. TPAMI 18, 377–388 (1996)
Guibas, L.J., Huang, Q., Liang, Z.: A condition number for joint optimization of cycle-consistent networks. In: NeurIPS (2019)
Hu, N., Huang, Q., Thibert, B., Guibas, L.J.: Distributable consistent multi-object matching. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2463–2471 (2018)
Hu, N., Rustamov, R.M., Guibas, L.: Graph matching with anchor nodes: a learning approach. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2906–2913 (2013)
Hu, N., Rustamov, R.M., Guibas, L.: Stable and informative spectral signatures for graph matching. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 2305–2312 (2014)
Huang, Q., Zhang, G., Gao, L., Hu, S., Butscher, A., Guibas, L.: An optimization approach for extracting and encoding consistent maps in a shape collection. ACM Trans. Graph. (TOG) 31, 1–11 (2012)
Kulesza, A., Taskar, B., Liu, L.: Determinantal point processes for machine learning. Found. Trends Mach. Learn. 5, 123–286 (2012)
Leordeanu, M., Sukthankar, R., Hebert, M.: Unsupervised learning for graph matching. IJCV 96, 28–45 (2012)
Leordeanu, M., Zanfir, A., Sminchisescu, C.: Semi-supervised learning and optimization for hypergraph matching. In: ICCV (2011)
Loiola, E.M., de Abreu, N.M., Boaventura-Netto, P.O., Hahn, P., Querido, T.: A survey for the quadratic assignment problem. EJOR 176, 657–690 (2007)
Ngoc, Q., Gautier, A., Hein, M.: A flexible tensor block coordinate ascent scheme for hypergraph matching. In: CVPR (2015)
Pachauri, D., Kondor, R., Vikas, S.: Solving the multi-way matching problem by permutation synchronization. In: NIPS (2013)
Shi, X., Ling, H., Hu, W., Xing, J., Zhang, Y.: Tensor power iteration for multi-graph matching. In: CVPR (2016)
Solé-Ribalta, A., Serratosa, F.: Models and algorithms for computing the common labelling of a set of attributed graphs. CVIU 115, 929–945 (2011)
Solé-Ribalta, A., Serratosa, F.: Graduated assignment algorithm for multiple graph matching based on a common labeling. IJPRAI 27, 1350001 (2013)
Swoboda, P., Mokarian, A., Theobalt, C., Bernard, F., et al.: A convex relaxation for multi-graph matching. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 11156–11165 (2019)
Vento, M.: A long trip in the charming world of graphs for pattern recognition. Pattern Recogn. 48(2), 291–301 (2015)
Wang, R., Yan, J., Yang, X.: Learning combinatorial embedding networks for deep graph matching. In: ICCV (2019)
Yan, J., Cho, M., Zha, H., Yang, X., Chu, S.: Multi-graph matching via affinity optimization with graduated consistency regularization. TPAMI 38, 1228–1242 (2016)
Yan, J., Li, Y., Liu, W., Zha, H., Yang, X., Chu, S.M.: Graduated consistency-regularized optimization for multi-graph matching. In: Fleet, D., Pajdla, T., Schiele, B., Tuytelaars, T. (eds.) ECCV 2014. LNCS, vol. 8689, pp. 407–422. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-10590-1_27
Yan, J., Tian, Y., Zha, H., Yang, X., Zhang, Y., Chu, S.: Joint optimization for consistent multiple graph matching. In: ICCV (2013)
Yan, J., Wang, J., Zha, H., Yang, X., Chu, S.: Consistency-driven alternating optimization for multigraph matching: a unified approach. IEEE Trans. Image Process. 24(3), 994–1009 (2015)
Yan, J., Xu, H., Zha, H., Yang, X., Liu, H., Chu, S.: A matrix decomposition perspective to multiple graph matching. In: ICCV (2015)
Yan, J., Yin, X., Lin, W., Deng, C., Zha, H., Yang, X.: A short survey of recent advances in graph matching. In: ICMR (2016)
Yan, J., Zhang, C., Zha, H., Liu, W., Yang, X., Chu, S.: Discrete hyper-graph matching. In: CVPR (2015)
Yu, T., Yan, J., Liu, W., Li, B.: Incremental multi-graph matching via diversity and randomness based graph clustering. In: Ferrari, V., Hebert, M., Sminchisescu, C., Weiss, Y. (eds.) ECCV 2018. LNCS, vol. 11217, pp. 142–158. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-01261-8_9
Zass, R., Shashua, A.: Probabilistic graph and hypergraph matching. In: CVPR (2008)
Zhang, Z.: Iterative point matching for registration of free-form curves and surfaces. IJCV 13, 119–152 (1994)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Chen, Z., Xie, Z., Yan, J., Zheng, Y., Yang, X. (2020). Layered Neighborhood Expansion for Incremental Multiple Graph Matching. In: Vedaldi, A., Bischof, H., Brox, T., Frahm, JM. (eds) Computer Vision – ECCV 2020. ECCV 2020. Lecture Notes in Computer Science(), vol 12355. Springer, Cham. https://doi.org/10.1007/978-3-030-58607-2_15
Download citation
DOI: https://doi.org/10.1007/978-3-030-58607-2_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-58606-5
Online ISBN: 978-3-030-58607-2
eBook Packages: Computer ScienceComputer Science (R0)