Efficient Alignment and Correspondence Using Edit Distance

  • Paolo Bergamini
  • Luigi Cinque
  • Andrew D. J. Cross
  • Edwin R. Hancock
  • Stefano Levialdi
  • Richard Myers
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1876)

Abstract

This paper presents work aimed at rendering the dual-step EM algorithm of Cross and Hancock more efficient. The original algorithm integrates the processes of point-set alignment and correspondence. The consistency of the pattern of correspondence matches on the Delaunay triangulation of the points is used to gate contributions to the expected log-likelihood function for point-set alignment parameters. However, in its original form the algorithm uses a dictionary of structure-preserving mappings to asses the consistency of match. This proves to be a serious computational bottleneck. In this paper, we show how graph edit-distance can be used to compute the correspondence probabilities more efficiently. In a sensitivity analysis, we show that the edit distance method is not only more efficient, it is also more accurate than the dictionary-based method.

Keywords

Delaunay Triangulation Edit Distance Computational Bottleneck Delaunay Graph Feasible Mapping 
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.
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References

  1. 1.
    A.D.J. Cross and E.R. Hancock, “Graph Matching with a Dual Step EM Algorithm”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 20, pp 1236–1253, 1998.CrossRefGoogle Scholar
  2. 2.
    A.P. Dempster, Laird N.M. and Rubin D.B., “Maximum-likelihood from incomplete data via the EM algorithm”, J. Royal Statistical Soc. Ser. B (methodological), 39, pp 1–38, 1977.MATHMathSciNetGoogle Scholar
  3. 3.
    O.D. Faugeras, E. Le Bras-Mehlman and J-D. Boissonnat, “Representing Stereo Data with the Delaunay Triangulation”, Artificial Intelligence, 44, pp. 41–87, 1990.CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Gold S., Rangarajan A. and Mjolsness E., “Learning with pre-knowledge: Clustering with point and graph-matching distance measures”, Neural Computation, 8, pp. 787–804, 1996.CrossRefGoogle Scholar
  5. 5.
    M.I. Jordan and R.A. Jacobs, “Hierarchical Mixtures of Experts and the EM Algorithm”, Neural Computation, 6, pp. 181–214, 1994.CrossRefGoogle Scholar
  6. 6.
    M. Lades, J.C. Vorbruggen, J. Buhmann, J. Lange, C. von der Maalsburg, R.P. Wurtz and W. Konen, “Distortion-invariant object-recognition in a dynamic link architecture”, IEEE Transactions on Computers, 42, pp. 300–311, 1993CrossRefGoogle Scholar
  7. 7.
    R. A. Wagner and M. J. Fischer, “The String-to-String Correction Problem”, Journal of the Association for Computing Machinery, 21, pp. 168–173, 1974.MATHMathSciNetGoogle Scholar
  8. 8.
    A. Marzal and E. Vidal, “Computation of Normalised Edit Distance and Applications”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 15, pp. 926–932, 1993.CrossRefGoogle Scholar
  9. 9.
    H. Bunke, and J. Csirik, “Parametric String Edit Distance and its application to Pattern Recognition”, IEEE Transactions on Systems, Man, and Cybernetics, 25, pp. 202–206, 1995.CrossRefGoogle Scholar
  10. 10.
    D.P. McReynolds and D.G. Lowe, “Rigidity Checking of 3D Point Correspondences under Perspective Projection”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 18, pp. 1174–1185, 1996.CrossRefGoogle Scholar
  11. 11.
    R. Myers, R.C. Wilson and E.R. Hancock, “Efficient Relational Matching with Local Edit Distance”, Proceedings of the Fourteenth International Conference on Pattern Recognition, IEEE Computer Society Press, pp 1711–1714, 1998.Google Scholar
  12. 12.
    D. Oberkampf, D.F. DeMenthon and L.S. Davis, “Iterative Pose Estimation using Coplanar Feature Points”, Computer Vision and Image Understanding, 63, pp. 495–511, 1996.CrossRefGoogle Scholar
  13. 13.
    R.C. Wilson and E.R. Hancock, “Structural Matching by Discrete Relaxation”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 19, pp. 634–648, 1997.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Paolo Bergamini
    • 1
  • Luigi Cinque
    • 1
  • Andrew D. J. Cross
    • 2
  • Edwin R. Hancock
    • 2
  • Stefano Levialdi
    • 1
  • Richard Myers
    • 2
  1. 1.Dip. di Scienze dell’InformazioneUniversità “La Sapienza”di RomaVia SalariaRome, IT
  2. 2.Dept. of Computer ScienceUniversity of YorkYorkUK

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