Abstract
Graph matching has a wide spectrum of computer vision applications such as finding feature point correspondences across images. The problem of graph matching is generally NP-hard, so most existing work pursues suboptimal solutions between two graphs. This paper investigates a more general problem of matching N attributed graphs to each other, i.e. labeling their common node correspondences such that a certain compatibility/affinity objective is optimized. This multi-graph matching problem involves two key ingredients affecting the overall accuracy: a) the pairwise affinity matching score between two local graphs, and b) global matching consistency that measures the uniqueness and consistency of the pairwise matching results by different sequential matching orders. Previous work typically either enforces the matching consistency constraints in the beginning of iterative optimization, which may propagate matching error both over iterations and across different graph pairs; or separates score optimizing and consistency synchronization in two steps. This paper is motivated by the observation that affinity score and consistency are mutually affected and shall be tackled jointly to capture their correlation behavior. As such, we propose a novel multi-graph matching algorithm to incorporate the two aspects by iteratively approximating the global-optimal affinity score, meanwhile gradually infusing the consistency as a regularizer, which improves the performance of the initial solutions obtained by existing pairwise graph matching solvers. The proposed algorithm with a theoretically proven convergence shows notable efficacy on both synthetic and public image datasets.
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References
Besl, P., McKay, N.: A method for registration of 3-d shapes. PAMI (1992)
Brendel, W., Todorovic, S.: Learning spatiotemporal graphs of human activities. In: ICCV (2011)
Caetano, T., McAuley, J., Cheng, L., Le, Q., Smola, A.J.: Learning graph matching. IEEE Transaction on PAMI 31(6), 1048–1058 (2009)
Chertok, M., Keller, Y.: Efficient high order matching. PAMI (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, Part V. LNCS, vol. 6315, pp. 492–505. Springer, Heidelberg (2010)
Cho, M., Lee, K.M.: Progressive graph matching: Making a move of graphs via probabilistic voting. In: CVPR (2012)
Cho, M., Sun, J., Duchenne, O., Ponce, J.: Finding matches in a haystack: A max-pooling strategy for graph matching in the presence of outliers. In: CVPR (2014)
Conte, D., Foggia, P., Sansone, C., Vento, M.: Thirty years of graph matching in pattern recognition. IJPRAI (2004)
Duchenne, O., Bach, F., Kweon, I., Ponce, J.: A tensor-based algorithm for high-order graph matching. In: CVPR (2009)
Eshera, M.A., Fu, K.S.: An image understanding system using attributed symbolic representation and inexact graph-matching. PAMI (1986)
Fischler, M., Bolles, R.: Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography. Comm. of the ACM, 381–395 (1981)
Foggia, P., Percannella, G., Vento, M.: Graph matching and learning in pattern recognition in the last 10 years. IJPRAI (2014)
Gallagher, B.: Matching structure and semantics: A survey on graph-based pattern matching. In: AAAI, pp. 45–53 (2006)
Garey, M.R., Johnson, D.S.: Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman and Co., New York (1990)
Gavril, F.: Generating the maximum spanning trees of a weighted graph. Journal of Algorithms, 592–597 (1987)
Goesele, M., Snavely, N., Curless, B., Hoppe, H., Seitz, S.: Multi-view stereo for community photo collections. In: ICCV (2007)
Gold, S., Rangarajan, A.: A graduated assignment algorithm for graph matching. IEEE Transaction on PAMI (1996)
Hancock, E.R., Wilson, R.C.: Pattern analysis with graphs: Parallel work at bern and york. Pattern Recognition Letters, 833–841 (2012)
Hu, N., Rustamov, R.M., Guibas, L.: Graph mmatching with anchor nodes: a learning approach. In: CVPR (2013)
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 Transactions on Graphics, TOG (2012)
Huang, Q.X., Flory, S., Gelfand, N., Hofer, M., Pottmann, H.: Reassembling fractured objects by geometric matching. ACM Trans. Graph., 569–578 (2006)
Kim, V.G., Li, W., Mitra, N.J., DiVerdi, S., Funkhouser, T.: Exploring collections of 3D models using fuzzy correspondences. In: SIGGRAPH (2012)
Kuhn, H.W.: The hungarian method for the assignment problem. Export. Naval Research Logistics Quarterly, 83–97 (1955)
Lee, J., Cho, M., Lee, K.M.: Hyper-graph matching via reweighted random walks. In: CVPR (2011)
Leordeanu, M., Hebert, M.: A spectral technique for correspondence problems using pairwise constraints. In: ICCV (2005)
Leordeanu, M., Hebert, M., Sukthankar, R.: Beyond local appearance: Category recognition from pairwise interactions of simple features. In: CVPR (2007)
Leordeanu, M., Herbert, M.: An integer projected fixed point method for graph matching and map inference. In: NIPS (2009)
Leordeanu, M., Sukthankar, R., Hebert, M.: Unsupervised learning for graph matching. Int. J. Comput. Vis., 28–45 (2012)
Leordeanu, M., Zanfir, A., Sminchisescu, C.: Semi-supervised learning and optimization for hypergraph matching. In: ICCV (2011)
Livi, L., Rizzi, A.: The graph matching problem. Pattern Anal. Applic., 253–283 (2013)
Loiola, E.M., de Abreu, N.M., Boaventura-Netto, P.O., Hahn, P., Querido, T.: A survey for the quadratic assignment problem. EJOR, 657–690 (2007)
Pachauri, D., Kondor, R., Vikas, S.: Solving the multi-way matching problem by permutation synchronization. In: NIPS (2013)
Pevzner, P.A.: Multiple alignment, communication cost, and graph matching. SIAM JAM (1992)
Qiu, H., Hancock, E.R.: Spectral simplification of graphs. In: Pajdla, T., Matas, J. (eds.) ECCV 2004. LNCS, vol. 3024, pp. 114–126. Springer, Heidelberg (2004)
Shen, D., Hammer, C.D.: Hierarchical attribute matching mechanism for elastic registration. TMI (2002)
Sole-Ribalta, A., Serratosa, F.: Graduated assignment algorithm for multiple graph matching based on a common labeling. IJPRAI (2013)
Suh, Y., Cho, M., Lee, K.M.: Graph matching via sequential monte carlo. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part III. LNCS, vol. 7574, pp. 624–637. Springer, Heidelberg (2012)
Cour, T., Srinivasan, P., Shi, J.: Balanced graph matching. In: NIPS (2006)
Tian, Y., Yan, J., Zhang, H., Zhang, Y., Yang, X., Zha, H.: On the convergence of graph matching: Graduated assignment revisited. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part III. LNCS, vol. 7574, pp. 821–835. Springer, Heidelberg (2012)
Williams, M.L., Wilson, R.C., Hancock, E.: Multiple graph matching with bayesian inference. Pattern Recognition Letters, 1275–1281 (1997)
Wong, A., You, M.: Entropy and distance of random graphs with application to structural pattern recognition. IEEE Transactions on PAMI (1985)
Yan, J., Li, Y., Zheng, E., Liu, Y.: An accelerated human motion tracking system based on voxel reconstruction under complex environments. In: Zha, H., Taniguchi, R.-I., Maybank, S. (eds.) ACCV 2009, Part II. LNCS, vol. 5995, pp. 313–324. Springer, Heidelberg (2010)
Yan, J., Tian, Y., Zha, H., Yang, X., Zhang, Y.: Joint optimization for consistent multiple graph matching. In: ICCV (2013)
Zach, C., Klopschitz, M., Pollefeys, M.: Disambiguating visual relations using loop constraints, pp. 1246–1433 (2010)
Zaslavskiy, M., Bach, F.R., Vert, J.P.: A path following algorithm for the graph matching problem. PAMI (2009)
Zass, R., Shashua, A.: Probabilistic graph and hypergraph matching. In: CVPR (2008)
Zeng, Z., Chan, T.-H., Jia, K., Xu, D.: Finding correspondence from multiple images via sparse and low-rank decomposition. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part V. LNCS, vol. 7576, pp. 325–339. Springer, Heidelberg (2012)
Zhou, F., Torre, F.D.: Factorized graph matching. In: CVPR (2012)
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Yan, J., Li, Y., Liu, W., Zha, H., Yang, X., Chu, S.M. (2014). Graduated Consistency-Regularized Optimization for Multi-graph Matching. In: Fleet, D., Pajdla, T., Schiele, B., Tuytelaars, T. (eds) Computer Vision – ECCV 2014. ECCV 2014. Lecture Notes in Computer Science, vol 8689. Springer, Cham. https://doi.org/10.1007/978-3-319-10590-1_27
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