Graph Matching Based on Fast Normalized Cut

  • Jing Yang
  • Xu YangEmail author
  • Zhang-Bing Zhou
  • Zhi-Yong Liu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11306)


Graph matching is important in pattern recognition and computer vision which can solve the point correspondence problems. Graph matching is an NP-hard problem and approximate relaxation methods are used to solve this problem. But most of the existing relaxation methods solve graph matching problem in the continues domain without considering the discrete constraints. In this paper, we propose a fast normalized cut based graph matching method which takes the discrete constraints into consideration. Specifically, a regularization term which is related to the discrete form of the permutation matrix is added to the objective function. Then, the objective function is transformed to a form which is similar to the fast normalized cut framework. The fast normalized cut algorithm is generalized to get the permutation matrix iteratively. The comparisons with the state-of-the-art methods validate the effectiveness of the proposed method by the experiments on synthetic data and image sequences.


Graph matching Fast normalized cut Discrete constraints 



This work is supported partly by the National Natural Science Foundation (NSFC) of China (grants 61772479, 61662021, 61773047, 61503383, 61633009, U1613213, 61627808, 61502494, and U1713201), partly by the National Key Research and Development Plan of China (grant 2016YFC0300801 and 2017YFB1300202), and partly by the Development of Science and Technology of Guangdong Province Special Fund project (grant 2016B090910001).


  1. 1.
    Achuurmans, D., Li, W., Xu, L.: Fast normalized cut with linear constraints. In: 22th IEEE Conference on Computer Vision and Pattern Recognition, pp. 2866–2873. Miami (2009)Google Scholar
  2. 2.
    Bryan, K., Leise, T.: The 25,000,000,000 eigenvetor: the linear algebra behind google. Siam Rev. 48(3), 569–581 (2006)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Cetano, T.S., MeAuley, 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.
    Cho, M., Lee, J., Lee, K.M.: Reweighted random walks for graph matching. In: 20th Conference and Workshop on Neural Information Processing Systems, pp. 313–320. Vancouver (2006)Google Scholar
  5. 5.
    Conte, D., Foggia, P., Sansone, C., Vento, M.: Thirty years of graph matching in pattern recognition. Int. J. Pattern Recognit. Artifical Intell. 18(3), 265–298 (2004)CrossRefGoogle Scholar
  6. 6.
    Cour, M., Srinivasan, P., Shi, J.: Balanced graph matching. In: 20th Conference and Workshop on Neural Information Processing Systems, pp. 313–320. Vancouver (2006)Google Scholar
  7. 7.
    Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun. Assoc. Comput. Mach. 24(6), 381–395 (1981)MathSciNetGoogle Scholar
  8. 8.
    Gold, S., Rangarajan, A.: A graduated assignment algorithm for graph matching. IEEE Trans. Pattern Anal. Mach. Intell. 18(4), 377–388 (1996)CrossRefGoogle Scholar
  9. 9.
    Hagen, L., Kahng, A.: New spectral methods for ratio cut partioning and clustering. IEEE Trans. Comput. Aided Des. Intergrated Circuits Syst. 11(9), 1074–1085 (1992)CrossRefGoogle Scholar
  10. 10.
    James, M.: Algorithms for the assignment and transportation problems. SIAM J. Appl. Math. 5(1), 32–38 (1957)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Jiang, B., Tang, J., Ding, C., Luo, B.: Binary constraint preserving graph matching. In: 30th IEEE Conference on Computer Vision and Pattern Recognition, pp. 550–557. Hawaii (2017)Google Scholar
  12. 12.
    Jiang, H., Yu, X.S., Martin, D.R.: Linear scale and rotation invariant matching. IEEE Trans. Pattern Anal. Mach. Intell. 33(7), 1339–1355 (2011)CrossRefGoogle Scholar
  13. 13.
    Leoedeanu, M., Hebert, M.: A spectral technique for correspondence problems using pairwise constraints. In: 10th IEEE Conference on International Conference on Computer Vision, pp. 1482–1489. Beijing (2005)Google Scholar
  14. 14.
    Leoedeanu, M., Hebert, M., Sukthankar, R.: An integer projected fixed point method for graph matching and map inference. In: 23th Conference and Workshop on Neural Information Processing Systems, pp. 1114–1122. Vancouver (2009)Google Scholar
  15. 15.
    Michel, D., Oikonomidis, I., Argyros, A.A.: Scale invariant and deformation tolerant partial shape matching. Image Vis. Comput. 29(7), 459–469 (2011)CrossRefGoogle Scholar
  16. 16.
    Shi, J.B., Jitendra, M.: Normalized cuts and image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 22(8), 888–905 (2000)CrossRefGoogle Scholar
  17. 17.
    Sullivan, J., Carlsson, S.: Recognizing and tracking human action. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2350, pp. 629–644. Springer, Heidelberg (2002). Scholar
  18. 18.
    Umeyama, S.: An eigendecomposition approach to weighted graph matching problems. IEEE Trans. Pattern Anal. Mach. Intell. 10(5), 695–703 (1988)CrossRefGoogle Scholar
  19. 19.
    Zass, R., Shashua, A.: Probabilistic graph and hypergraph matching, In: 21th IEEE Conference on Computer Vision and Pattern Recognition, pp. 1-8. Anchorage(2008)Google Scholar
  20. 20.
    Zhang, Z.Y.: Iterative point matching for registration of free-form curves and surfaces. Int. J. Comput. Vis. 13(2), 119–152 (1994)CrossRefGoogle Scholar
  21. 21.
    Zhou, F., De la Torre, F.: Factorized graph matching. In: 25th IEEE Conference on Computer Vision and Pattern Recognition, pp. 127–134. Providence (2012)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Jing Yang
    • 1
    • 2
  • Xu Yang
    • 2
    Email author
  • Zhang-Bing Zhou
    • 1
    • 3
  • Zhi-Yong Liu
    • 2
    • 4
    • 5
  1. 1.School of Information EngineeringChina University of Geosciences (Beijing)BeijingChina
  2. 2.State Key Laboratory of Management and Control for Complex Systems, Institute of AutomationChinese Academy of SciencesBeijingChina
  3. 3.Computer Science DepartmentTELECOM SudParisEvryFrance
  4. 4.Center for Excellence in Brain Science and Intelligence TechnologyChinese Academy of SciencesShanghaiChina
  5. 5.University of Chinese Academy of SciencesBeijingChina

Personalised recommendations