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An Auction Algorithm for Graph-Based Contextual Correspondence Matching

  • Barend J. van Wyk
  • Michaël A. van Wyk
  • Guillaume Noel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3138)

Abstract

The Auction Graph Matching (AUGM) algorithm is presented. This algorithm is based on a novel joint probabilistic framework that transforms the graph matching problem into a linear assignment problem which is efficiently solved by the Bertsekas auction algorithm. A salient feature of this single-pass auction-based approach is that the inferred match probabilities are not only constrained over all objects in the reference image, but are also constrained over all objects in the input image.

Keywords

Joint Probability Input Graph Graph Match Quadratic Assignment Problem Compatibility Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Gold, S., Rangarajan, A.: A Graduated Assignment Algorithm for Graph Matching. IEEE Trans. Patt. Anal. Machine Intell. 18(4), 377–388 (1996)CrossRefGoogle Scholar
  2. 2.
    Simić, P.D.: Constrained Nets for Graph Matching and Other Quadratic Assignment Problems. Neural Computation 3, 268–281 (1991)CrossRefGoogle Scholar
  3. 3.
    Van Wyk, B.J.: Kronecker Product, Successive Projection, and Related Graph Matching Algorithms, PhD Thesis, University of the Witwatersrand, Johannesburg (2003), http://www.ee.wits.ac.za/comms/output/theses.htm
  4. 4.
    Bertsekas, D.P.: The Auction Algorithm for Assignment and Other Network Flow Problems: A Tutorial. Interfaces 20, 133–149 (1990)CrossRefGoogle Scholar
  5. 5.
    Jonker, R., Volgenant, A.: A Shortest Augmenting Path Algorithm for Dense and Sparse Linear Assignment Problems. Computing 38, 325–340 (1987)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Christmas, W.J., Kittler, J., Petrou, M.: Structural Matching in Computer Vision using Probabilistic Relaxation. IEEE Trans. Patt. Anal. Machine Intell. 17(8), 749–764 (1995)CrossRefGoogle Scholar
  7. 7.
    Cross, A.D.J., Hancock, E.R.: Graph Matching with a Dual Step EM Algorithm. IEEE Transactions on Pattern Analysis and Machine Intelligence 20(11), 1236–1253 (1998)CrossRefGoogle Scholar
  8. 8.
    Kittler, J., Petrou, M., Christmas, W.J.: A Non-iterative Probabilistic Method for Contextual Correspondence Matching. Pattern Recognition 31, 1455–1468 (1998)CrossRefGoogle Scholar
  9. 9.
    Finch, A.M., Wilson, R.C., Hancock, R.: Symbolic Matching with the EM Algorithm. Pattern Recognition 31(11), 1777–1790 (1998)CrossRefGoogle Scholar
  10. 10.
    Williams, M.L., Wilson, R.C., Hancock, E.R.: Multiple Graph Matching with Bayesian Inference. Pattern Recognition Letters 18, 1275–1281 (1997)CrossRefGoogle Scholar
  11. 11.
    Cross, A.D.J., Hancock, E.R.: Graph Matching with a Dual Step EM Algorithm. IEEE Trans. Patt. Anal. Machine Intell. 20(11), 1236–1253 (1998)CrossRefGoogle Scholar
  12. 12.
    Wilson, R.C., Hancock, E.R.: A Bayesian Compatibility Model for Graph Matching. Pattern Recognition Letters 17, 263–276 (1996)CrossRefGoogle Scholar
  13. 13.
    Wilson, R.C., Hancock, E.R.: Structural Matching by Discrete Relaxation. IEEE Trans. Patt. Anal. Machine Intell. 19(6), 634–648 (1997)CrossRefGoogle Scholar
  14. 14.
    Finch, A.M., Wilson, R.C., Hancock, E.R.: Matching Delauney Triangulations by Probabilistic Relaxation. In: Hlaváč, V., Šára, R. (eds.) CAIP 1995. LNCS, vol. 970, pp. 351–358. Springer, Heidelberg (1995)Google Scholar
  15. 15.
    Meyers, R.M., Wilson, R.C., Hancock, E.R.: Bayesian Graph Edit Distance. IEEE Trans. Patt. Anal. Machine Intell. 2(6), 628–635 (2000)CrossRefGoogle Scholar
  16. 16.
    Faugeras, O.D., Price, K.E.: Semantic Description of Aerial Images Using Stochastic Labeling. IEEE Transactions on Pattern Analysis and Machine Intelligence 3(6), 633–642 (1981)CrossRefGoogle Scholar
  17. 17.
    Van Wyk, B.J., Van Wyk, M.A., Botha, J.J.: A Matching Framework Based On Joint Probabilities. In: Proceedings of PRASA 2003, Langebaan, South Africa, November 27-28, pp. 125–130 (2003)Google Scholar
  18. 18.
    Caelli, T.M., Caetano, T.: Recent Developments in the Extraction and Matching of Image Structure and Syntax: From Relaxation to Junction Tree Models. In: Proceedings of PRASA 2003, Langebaan, South Africa, November 27-28, pp. 1–8 (2003)Google Scholar
  19. 19.
    Li, S.Z.: Matching: Invariant to Translations Rotations and Scale Changes. Pattern Recognition 25(6), 583–594 (1992)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Barend J. van Wyk
    • 1
  • Michaël A. van Wyk
    • 1
  • Guillaume Noel
    • 1
  1. 1.French South-African Technical Institute in ElectronicsTshwane University of TechnologyPretoriaSouth Africa

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