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Issue No.11 - November (2008 vol.30)
pp: 2047-2054
Julian J. McAuley , NICTA, Canberra
Tibério S. Caetano , NICTA, Canberra
Marconi S. Barbosa , NICTA, Canberra
ABSTRACT
A recent paper \cite{CaeCaeSchBar06} proposed a provably optimal, polynomial time method for performing near-isometric point pattern matching by means of exact probabilistic inference in a chordal graphical model. Its fundamental result is that the chordal graph in question is shown to be \emph{globally rigid}, implying that exact inference provides the \emph{same} matching solution as exact inference in a complete graphical model. This implies that the algorithm is optimal when there is no noise in the point patterns. In this paper, we present a new graph which is also globally rigid but has an advantage over the graph proposed in \cite{CaeCaeSchBar06}: its maximal clique size is smaller, rendering inference significantly more efficient. However, this graph is not chordal and thus standard Junction Tree algorithms cannot be directly applied. Nevertheless, we show that loopy belief propagation in such a graph converges to the optimal solution. This allows us to retain the optimality guarantee in the noiseless case, while substantially reducing both memory requirements and processing time. Our experimental results show that the accuracy of the proposed solution is indistinguishable from that of \cite{CaeCaeSchBar06} when there is noise in the point patterns.
INDEX TERMS
Point pattern matching, graph matching, graphical models, belief propagation, global rigidity, chordal graphs
CITATION
Julian J. McAuley, Tibério S. Caetano, Marconi S. Barbosa, "Graph Rigidity, Cyclic Belief Propagation, and Point Pattern Matching", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.30, no. 11, pp. 2047-2054, November 2008, doi:10.1109/TPAMI.2008.124
REFERENCES
[1] T.S. Caetano, T. Caelli, D. Schuurmans, and D.A.C. Barone, “Graphical Models and Point Pattern Matching,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 28, no. 10, pp. 1646-1663, Oct. 2006.
[2] Y. Amit and A. Kong, “Graphical Templates for Model Registration,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 3, pp. 225-236, Mar. 1996.
[3] M. Carcassoni and E.R. Hancock, “Point Pattern Matching with Robust Spectral Correspondence,” Computer Vision and Pattern Recognition, vol. 1, p.1649, 2000.
[4] S. Belongie, J. Malik, and J. Puzicha, “Shape Matching and Object Recognition Using Shape Contexts,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 4, pp. 509-522, Apr. 2002.
[5] A. Robles-Kelly and E.R. Hancock, “Point Pattern Matching via Spectral Geometry,” Syntactical and Structural Pattern Recognition, Statistical Pattern Recognition, pp. 459-467, 2006.
[6] A. Rangarajan, J. Coughlan, and A.L. Yuille, “A Bayesian Network Framework for Relational Shape Matching,” Proc. Int'l Conf. Computer Vision (ICCV '03), p. 671, 2003.
[7] P.F. Felzenszwalb, “Representation and Detection of Deformable Shapes,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 2, pp. 208-220, Feb. 2005.
[8] D. Crandall, P. Felzenszwalb, and D. Huttenlocher, “Spatial Priors for Part-Based Recognition Using Statistical Models,” Proc. Int'l Conf. Computer Vision and Pattern Recognition (CVPR '05), vol. 1, pp. 10-17, 2005.
[9] R. Connelly, “Generic Global Rigidity,” Discrete and Computational Geometry, vol. 33, no. 4, pp. 549-563, 2005.
[10] S. Gold and A. Rangarajan, “A Graduated Assignment Algorithm for Graph Matching,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 4, pp. 377-388, Apr. 1996.
[11] S.L. Lauritzen, Graphical Models (Oxford Statistical Science Series). Oxford Univ. Press, July 1996.
[12] C.M. Bishop, Pattern Recognition and Machine Learning (Information Science and Statistics). Springer, Aug. 2006.
[13] T.S. Caetano and T. Caelli, “A Unified Formulation of Invariant Point Pattern Matching,” Proc. Int'l Conf. Pattern Recognition (ICPR '06), pp. 121-124, 2006.
[14] Y. Weiss, “Correctness of Local Probability Propagation in Graphical Models with Loops,” Neural Computation, vol. 12, pp.1-41, 2000.
[15] A.T. Ihler, J.W. Fisher, and A.S. Willsky, “Message Errors in Belief Propagation,” Advances in Neural Information Processing Systems, pp. 609-616, 2005.
[16] Y. Weiss and W.T. Freeman, “On the Optimality of Solutions of the Max-Product Belief-Propagation Algorithm in Arbitrary Graphs,” IEEE Trans. Information Theory, vol. 47, 2001.
[17] J.S. Yedidia, W.T. Freeman, and Y. Weiss, “Generalized Belief Propagation,” Advances in Neural Information Processing Systems, pp. 689-695, 2000.
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