Abstract
We present a probabilistic graphical model for point set matching. By using a result about the redundancy of the pairwise distances in a point set, we represent the binary relations over a simple triangulated graph that retains the same informational content as the complete graph. The maximal clique size of this resultant graph is independent of the point set sizes, what enables us to perform exact inference in polynomial time with a Junction Tree algorithm. The resulting technique is optimal in the Maximum a Posteriori sense. Experiments show that the algorithm significantly outperforms standard probabilistic relaxation labeling.
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References
Carcassoni, M., Hancock, E.R.: Spectral correspondence for point pattern matching. Pattern Recognition 36, 193–204 (2003)
Luo, B., Hancock, E.R.: Structural Graph Matching using the EM Algorithm and Singular Value Decomposition. IEEE Trans. PAMI 23(10), 1120–1136 (2001)
Akutsu, T., Kanaya, K., Ohyama, A., Fujiyama, A.: Point matching under nonuniform distortions. Discrete Applied Mathematics 127, 5–21 (2003)
Reimann, D., Haken, H.: Stereo Vision by Self-Organization. Biological Cybernetics 74(1), 17–21 (1994)
Gold, S., Rangarajan, A.: A Graduated Assignment Algorithm for Graph Matching. IEEE Trans. PAMI 18(4), 377–388 (1996)
Lauritzen, S.L.: Graphical Models. Oxford University Press, New York (1996)
Jordan, M.I.: An Introduction to Probabilistic Graphical Models (in preparation)
Christmas, W.J., Kittler, J., Petrou, M.: Structural Matching in Computer Vision Using Probabilistic Relaxation. IEEE Trans. PAMI 17(8), 749–764 (1995)
Rosenfeld, A., Kak, A.C.: Digital Picture Processing, vol. 1. Academic Press, New York (1982)
Geman, S., Geman, D.: Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images. IEEE Trans. PAMI 6(6), 721–741 (1984)
de Rezende, P.J., Lee, D.T.: Point Set Pattern Matching in d-dimensions. Algorithmica 13, 387–404 (1995)
Connelly, R.: Generic Global Rigidity. Preprint privately provided
Jackson, B., Jordán, T.: Connected Rigidity Matroids and Unique Realizations of Graphs, citeseer.nj.nec.com/jackson03connected.html
West, D.B.: Introduction to Graph Theory, 2nd edn., Upper Saddle River, NJ. Prentice Hall, Englewood Cliffs (2001)
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© 2004 Springer-Verlag Berlin Heidelberg
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Caetano, T.S., Caelli, T., Barone, D.A.C. (2004). An Optimal Probabilistic Graphical Model for Point Set Matching. In: Fred, A., Caelli, T.M., Duin, R.P.W., Campilho, A.C., de Ridder, D. (eds) Structural, Syntactic, and Statistical Pattern Recognition. SSPR /SPR 2004. Lecture Notes in Computer Science, vol 3138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27868-9_16
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DOI: https://doi.org/10.1007/978-3-540-27868-9_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22570-6
Online ISBN: 978-3-540-27868-9
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