Many-to-Many Matching under the l1 Norm

  • M. Fatih Demirci
  • Yusuf Osmanlıoğlu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5716)


The problem of object recognition can be formulated as matching feature sets of different objects. Segmentation errors and scale difference result in many-to-many matching of feature sets, rather than one-to-one. This paper extends a previous algorithm on many-to-many graph matching. The proposed work represents graphs, which correspond to objects, isometrically in the geometric space under the l 1 norm. Empirical evaluation of the algorithm on a set of recognition trails, including a comparison with the previous approach, demonstrates the efficacy of the overall framework.


graph embedding Earth Mover’s Distance graph matching object recognition 


  1. 1.
    Agarwala, R., Bafna, V., Farach, M., Paterson, M., Thorup, M.: On the approximability of numerical taxonomy (fitting distances by tree metrics. SIAM Journal on Computing 28(2), 1073–1085 (1999)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Ahuja, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows: Theory, Algorithms, and Applications, pp. 4–7. Prentice Hall, Englewood Cliffs (1993)zbMATHGoogle Scholar
  3. 3.
    Almohamad, H.A., Duffuaa, S.O.: A linear programming approach for the weighted graph matching problem. IEEE Transactions on Pattern Analysis and Machine Intelligence 15(5), 522–525 (1993)CrossRefGoogle Scholar
  4. 4.
    Bell, E.T.: Exponential numbers. American Mathematics Monthly 41, 411–419 (1934)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Bunke, H.: Error correcting graph matching: On the influence of the underlying cost function. IEEE Transactions on Pattern Analysis and Machine Intelligence 21(9), 917–922 (1999)CrossRefGoogle Scholar
  6. 6.
    Demirci, F., Shokoufandeh, A., Keselman, Y., Bretzner, L., Dickinson, S.: Object recognition as many-to-many feature matching. International Journal of Computer Vision 69(2), 203–222 (2006)CrossRefzbMATHGoogle Scholar
  7. 7.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman & Co, New York (1979)zbMATHGoogle Scholar
  8. 8.
    Gupta, A.: Embedding tree metrics into low dimensional euclidean spaces. In: STOC 1999: Proceedings of the thirty-first annual ACM symposium on Theory of computing, pp. 694–700. ACM, New York (1999)CrossRefGoogle Scholar
  9. 9.
    Gupta, A.: Embedding tree metrics into low-dimensional euclidean spaces. Discrete & Computational Geometry 24(1), 105–116 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Hoffmann, C.M.: Group-theoretic algorithms and graph isomorphism. Springer, Berlin (1982)CrossRefzbMATHGoogle Scholar
  11. 11.
    Horaud, R., Skordas, T.: Structural matching for stereo vision. In: Nineth International Conference on Pattern Recognition, Rome, Italy, pp. 439–445 (1988)Google Scholar
  12. 12.
    Lee, S.W., Kim, J.H.: Attributed stroke graph matching for seal imprint verification. Pattern Recognition Letters 9, 137–145 (1989)CrossRefGoogle Scholar
  13. 13.
    Ling, H., Okada, K.: An efficient earth mover’s distance algorithm for robust histogram comparison. IEEE Transactions on Pattern Analysis and Machine Intelligence 29(5), 840–853 (2007)CrossRefGoogle Scholar
  14. 14.
    Rubner, Y., Tomasi, C., Guibas, L.J.: The earth mover’s distance as a metric for image retrieval. International Journal of Computer Vision 40(2), 99–121 (2000)CrossRefzbMATHGoogle Scholar
  15. 15.
    Siddiqi, K., Shokoufandeh, A., Dickinson, S., Zucker, S.: Shock graphs and shape matching. International Journal of Computer Vision 35(1), 13–32 (1999)CrossRefGoogle Scholar
  16. 16.
    Wang, Y.K., Fan, K.C., Horng, J.T.: Genetic-based search for error-correcting graph isomorphism. IEEETSMC: IEEE Transactions on Systems, Man, and Cybernetics 27 (1997)Google Scholar
  17. 17.
    Williams, M.L., Wilson, R.C., Hancock, E.R.: Deterministic search for relational graph matching. Pattern Recognition 32(7), 1255–1271 (1999)CrossRefGoogle Scholar
  18. 18.
    Wong, E.K.: Model matching in robot vision by subgraph isomorphism. Pattern Recognition 25(3), 287–303 (1992)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • M. Fatih Demirci
    • 1
  • Yusuf Osmanlıoğlu
    • 1
  1. 1.Computer Engineering DepartmentTOBB University of Economics and TechnologyAnkaraTurkey

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