Advertisement

Adaptively Transforming Graph Matching

  • Fudong Wang
  • Nan Xue
  • Yipeng Zhang
  • Xiang Bai
  • Gui-Song Xia
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11220)

Abstract

Recently, many graph matching methods that incorporate pairwise constraint and that can be formulated as a quadratic assignment problem (QAP) have been proposed. Although these methods demonstrate promising results for the graph matching problem, they have high complexity in space or time. In this paper, we introduce an adaptively transforming graph matching (ATGM) method from the perspective of functional representation. More precisely, under a transformation formulation, we aim to match two graphs by minimizing the discrepancy between the original graph and the transformed graph. With a linear representation map of the transformation, the pairwise edge attributes of graphs are explicitly represented by unary node attributes, which enables us to reduce the space and time complexity significantly. Due to an efficient Frank-Wolfe method-based optimization strategy, we can handle graphs with hundreds and thousands of nodes within an acceptable amount of time. Meanwhile, because transformation map can preserve graph structures, a domain adaptation-based strategy is proposed to remove the outliers. The experimental results demonstrate that our proposed method outperforms the state-of-the-art graph matching algorithms.

Keywords

Graph matching Transformation representation Frank-Wolfe method 

Notes

Acknowledgement

This research is supported by projects of National Natural Science Foundation of China (NSFC) under the contracts No.61771350 and No.41501462.

References

  1. 1.
    Belongie, S.J., Malik, J., Puzicha, J.: Shape matching and object recognition using shape contexts. IEEE Trans. Pattern Anal. Mach. Intell. 24(4), 509–522 (2002)CrossRefGoogle Scholar
  2. 2.
    Bougleux, S., Brun, L., Carletti, V., Foggia, P., Gaüzère, B., Vento, M.: Graph edit distance as a quadratic assignment problem. Pattern Recognit. Lett. 87, 38–46 (2017)CrossRefGoogle Scholar
  3. 3.
    Caetano, T.S., McAuley, J.J., Cheng, L., Le, Q.V., Smola, A.J.: Learning graph matching. IEEE Trans. Pattern Anal. Mach. Intell. 31(6), 1048–1058 (2009)CrossRefGoogle Scholar
  4. 4.
    Candès, E.J., Wakin, M.B., Boyd, S.P.: Enhancing sparsity by reweighted \(l_1\) minimization. J. Fourier Anal. Appl. 14(5), 877–905 (2008)Google Scholar
  5. 5.
    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_36CrossRefGoogle Scholar
  6. 6.
    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)Google Scholar
  7. 7.
    Cour, T., Srinivasan, P., Shi, J.: Balanced graph matching. In: NIPS (2006)Google Scholar
  8. 8.
    Courty, N., Flamary, R., Tuia, D., Rakotomamonjy, A.: Optimal transport for domain adaptation. IEEE Trans. Pattern Anal. Mach. Intell. 39(9), 1853–1865 (2017)CrossRefGoogle Scholar
  9. 9.
    Duchenne, O., Joulin, A., Ponce, J.: A graph-matching kernel for object categorization. In: ICCV (2011)Google Scholar
  10. 10.
    Egozi, A., Keller, Y., Guterman, H.: A probabilistic approach to spectral graph matching. IEEE Trans. Pattern Anal. Mach. Intell. 35(1), 18–27 (2013)CrossRefGoogle Scholar
  11. 11.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & company, New York (1979)Google Scholar
  12. 12.
    Garro, V., Giachetti, A.: Scale space graph representation and Kernel matching for non rigid and textured 3D shape retrieval. IEEE Trans. Pattern Anal. Mach. Intell. 38(6), 1258–1271 (2016)CrossRefGoogle Scholar
  13. 13.
    Gold, S., Rangarajan, A.: A graduated assignment algorithm for graph matching. IEEE Trans. Pattern Anal. Mach. Intell. 18(4), 377–388 (1996)CrossRefGoogle Scholar
  14. 14.
    Goldstein, A.A.: On steepest descent. SIAM J. Control Optim. 3(1), 147–151 (1965)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Jiang, B., Tang, J., Ding, C., Luo, B.: Binary constraint preserving graph matching. In: CVPR (2017)Google Scholar
  16. 16.
    Jonker, R., Volgenant, A.: A shortest augmenting path algorithm for dense and sparse linear assignment problems. Computing 38(4), 325–340 (1987)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Kuhn, H.W.: The Hungarian method for the assignment problem. In: 50 Years of Integer Programming 1958–2008 - From the Early Years to the State-of-the-Art, pp. 29–47. Springer, Berlin (2010)Google Scholar
  18. 18.
    Lacoste-Julien, S., Jaggi, M.: On the global linear convergence of Frank-Wolfe optimization variants. In: NIPS (2015)Google Scholar
  19. 19.
    Lê-Huu, D.K., Paragios, N.: Alternating direction graph matching. In: CVPR (2017)Google Scholar
  20. 20.
    Lee, J., Cho, M., Lee, K.M.: A graph matching algorithm using data-driven Markov chain Monte Carlo sampling. In: ICPR (2010)Google Scholar
  21. 21.
    Lee, J., Cho, M., Lee, K.M.: Hyper-graph matching via reweighted random walks. In: CVPR (2011)Google Scholar
  22. 22.
    Leordeanu, M., Hebert, M.: A spectral technique for correspondence problems using pairwise constraints. In: ICCV (2005)Google Scholar
  23. 23.
    Leordeanu, M., Hebert, M., Sukthankar, R.: An integer projected fixed point method for graph matching and map inference. In: NIPS (2009)Google Scholar
  24. 24.
    Leordeanu, M., Sukthankar, R., Hebert, M.: Unsupervised learning for graph matching. Int. J. Comput. Vis. 96(1), 28–45 (2012)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Liu, Z.Y., Qiao, H.: GNCCP—graduated nonconvexity and concavity procedure. IEEE Trans. Pattern Anal. Mach. Intell. 36(6), 1258–1267 (2014)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Liu, Z., Qiao, H., Yang, X., Hoi, S.C.H.: Graph matching by simplified convex-concave relaxation procedure. Int. J. Comput. Vis. 109(3), 169–186 (2014)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Loiola, E.M., de Abreu, N.M.M., Netto, P.O.B., Hahn, P., Querido, T.M.: A survey for the quadratic assignment problem. Eur. J. Oper. Res. 176(2), 657–690 (2007)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Pelillo, M., Siddiqi, K., Zucker, S.W.: Matching hierarchical structures using association graphs. IEEE Trans. Pattern Anal. Mach. Intell. 21(11), 1105–1120 (1999)CrossRefGoogle Scholar
  29. 29.
    Pinheiro, M.A., Kybic, J., Fua, P.: Geometric graph matching using Monte Carlo tree search. IEEE Trans. Pattern Anal. Mach. Intell. 39(11), 2171–2185 (2017)CrossRefGoogle Scholar
  30. 30.
    Riesen, K., Bunke, H.: Reducing the dimensionality of dissimilarity space embedding graph Kernels. Eng. Appl. AI 22(1), 48–56 (2009)Google Scholar
  31. 31.
    Shen, T., Zhu, S., Fang, T., Zhang, R., Quan, L.: Graph-based consistent matching for structure-from-motion. In: Leibe, B., Matas, J., Sebe, N., Welling, M. (eds.) ECCV 2016. LNCS, vol. 9907, pp. 139–155. Springer, Cham (2016).  https://doi.org/10.1007/978-3-319-46487-9_9CrossRefGoogle Scholar
  32. 32.
    Torresani, L., Kolmogorov, V., Rother, C.: A dual decomposition approach to feature correspondence. IEEE Trans. Pattern Anal. Mach. Intell. 35(2), 259–271 (2013)CrossRefGoogle Scholar
  33. 33.
    Xue, N., Xia, G., Bai, X., Zhang, L., Shen, W.: Anisotropic-scale junction detection and matching for indoor images. IEEE Trans. Image Process. 27(1), 78–91 (2018)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Yan, J., Yin, X., Lin, W., Deng, C., Zha, H., Yang, X.: A short survey of recent advances in graph matching. In: ICMR (2016)Google Scholar
  35. 35.
    Yan, J., Zhang, C., Zha, H., Liu, W., Yang, X., Chu, S.M.: Discrete hyper-graph matching. In: CVPR (2015)Google Scholar
  36. 36.
    Yao, B., Fei-Fei, L.: Action recognition with exemplar based 2.5D graph matching. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012. LNCS, vol. 7575, pp. 173–186. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-33765-9_13CrossRefGoogle Scholar
  37. 37.
    Yu, J.G., Xia, G.S., Samal, A., Tian, J.: Globally consistent correspondence of multiple feature sets using proximal Gauss Seidel relaxation. Pattern Recognit. 51, 255–267 (2016)CrossRefGoogle Scholar
  38. 38.
    Zaslavskiy, M., Bach, F.R., Vert, J.: A path following algorithm for the graph matching problem. IEEE Trans. Pattern Anal. Mach. Intell. 31(12), 2227–2242 (2009)CrossRefGoogle Scholar
  39. 39.
    Zass, R., Shashua, A.: Probabilistic graph and hypergraph matching. In: CVPR (2008)Google Scholar
  40. 40.
    Zhou, F., la Torre, F.D.: Factorized graph matching. IEEE Trans. Pattern Anal. Mach. Intell. 38(9), 1774–1789 (2016)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Fudong Wang
    • 1
  • Nan Xue
    • 1
  • Yipeng Zhang
    • 2
  • Xiang Bai
    • 3
  • Gui-Song Xia
    • 1
  1. 1.State Key Laboratory LIESMARSWuhan UniversityWuhanChina
  2. 2.School of Computer ScienceWuhan UniversityWuhanChina
  3. 3.EIS, Huazhong University of Science and TechnologyWuhanChina

Personalised recommendations