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A POCS-Based Graph Matching Algorithm
November 2004 (vol. 26 no. 11)
pp. 1526-1530
A novel Projections Onto Convex Sets (POCS) graph matching algorithm is presented. Two-way assignment constraints are enforced without using elaborate penalty terms, graduated nonconvexity, or sophisticated annealing mechanisms to escape from poor local minima. Results indicate that the presented algorithm is robust and compares favorably to other well-known algorithms.

[1] B.T. Messmer and H. Bunke, “A New Algorithm for Error-Tolerant Subgraph Isomorphism Detection,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 5, pp. 493-504, May 1998.
[2] B.J. Van Wyk and M.A. Van Wyk, Kronecker Product Graph Matching Pattern Recognition J., vol. 36, no. 9, pp. 2019-2030, 2003.
[3] 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.
[4] A. Rosenfeld, R.A. Hummel, and S.W. Zucker, Scene Labeling by Relaxation Operations IEEE Trans. Systems, Man, and Cybernetics, vol. 6, no. 6, pp. 420-433, 1976.
[5] O.D. Faugeras and K.E. Price, Semantic Description of Aerial Images Using Stochastic Labeling IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 3, no. 6, pp. 633-642, 1981.
[6] R.A. Hummel and S.W. Zucker, On The Foundations of Relaxation Labeling Procesesses IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 5, no. 3, pp. 267-286, 1983.
[7] K.E. Price, Relaxation Labeling Techniques IEEE Trans. Pattern Analysis and Machine Intelligence vol. 7, no. 5, pp. 617-623, 1985.
[8] W.J. Christmas, J. Kittler, and M. Petrou, “Structural Matching in Computer Vision Using Probabilistic Relaxation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 17, no. 8, pp. 749–764, Aug. 1995.
[9] J. Kittler, M. Petrou, and W.J. Christmas, A Noniterative Probabilistic Method for Contextual Correspondence Matching Pattern Recognition, vol. 31, pp. 1455-1468, 1998.
[10] A.M. Finch, R.C. Wilson, and E.R. Hancock, Symbolic Matching with the EM Algorithm Pattern Recognition, vol. 31, no. 11, pp. 1777-1790, 1998.
[11] M.L. Williams, R.C. Wilson, and E.R. Hancock, Multiple Graph Matching with Bayesian Inference Pattern Recognition Letters, vol. 18, pp. 1275-1281, 1997.
[12] R.C. Wilson and E.R. Hancock, A Bayesian Compatibility Model for Graph Matching Pattern Recognition Letters, vol. 17, pp. 263-276, 1996.
[13] E. Mjolsness, G. Gindi, and P. Anandan, Optimization in Model Matching and Perceptual Organization Neural Computation, vol. 1, pp. 218-229, 1989.
[14] E. Mjolsness and C. Garrett, Algebraic Transformations of Objective Functions Neural Networks, vol. 3, pp. 651-669, 1990.
[15] P.D. Simi, Constrained Nets for Graph Matching and Other Quadratic Assignment Problems, Neural Computation, vol. 3, pp. 268-281, 1991.
[16] S.-S. Yu and W.-H. Tsai, Relaxation by the Hopfield Neural Network Pattern Recognition, vol. 25, no. 2, pp. 197-209, 1992.
[17] T.-W. Chen and W.-C. Lin, A Neural Network Approach to CSG-Based 3-D Object Recognition IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 16, no. 7, pp. 719-726, July 1994.
[18] P.N. Suganthan, H. Yan, E.K. Teoh, and D.P. Mital, Optimal Encoding of Graph Homomorphism Energy Using Fuzzy Information Aggregation Operators Pattern Recognition, vol. 31, no. 5, pp. 623-639, 1998.
[19] M. Peng and N. Gupta, Invariant and Occluded Object Recognition Based on Graph Matching Int'l J. Electrical Eng. Education, vol. 32, pp. 31-38, 1995.
[20] Y.-L. Lee and R.-H. Park, A Surface-based Approach to 3-D Object Recognition Using a Mean Field Annealing Neural Network Pattern Recognition, vol. 35, pp. 299-316, 2002.
[21] A. Rangarajan, A. Yuille, and E. Mjolsness, Convergence Properties of the Sofassign Quadratic Assignment Algorithm Neural Computation, vol. 11, pp. 1455-1474, 1999.
[22] M. Pelillo, Replicator Equations, Maximal Cliques, and Graph Isomorphism Neural Computation, vol. 11, pp. 1933-1955, 1999.
[23] B.J. VanWyk, M.A. VanWyk, and H.E. Hanrahan, Successive Projection Graph Matching Proc. Joint IAPR Int'l Workshops Syntactical and Structural Pattern Recognition and Statistical Pattern Recognition, T. Caelli et al., eds., pp. 263-271, 2002.
[24] H. Stark and Y. Yang, Vector Space Projections: A Numerical Approach to Signal and Image Processing, Neural Nets, and Optics. John Wiley and Sons, 1998.
[25] D.C. Youla, Mathematical Theory of Image Restoration by the Method of Convex Projections Image Recovery: Theory and Applications, Chapter 2, H. Stark, ed., 1987.
[26] B.J. Van Wyk, Kronecker Product, Successive Projection, and Related Graph Matching Algorithms PhD Thesis, Univ. of the Witwatersrand, Johannesburg, 2003, http://www.ee.wits.ac.za/comms/outputtheses.htm .
[27] A.M. Finch, R.C. Wilson, and E.R. Hancock, Matching Delauney Triangulations by Probabilistic Relaxation Proc. Conf. Computer Analysis of Images and Patterns, pp. 350-358, 1995.
[28] S. Peleg, A New Probabilistic Relaxation Scheme IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 2, no. 4, pp. 362-369, 1980.
[29] S.Z. Li, Matching: Invariant to Translations Rotations and Scale Changes Pattern Recognition, vol. 25, no. 6, pp. 583-594, 1992.
[30] B.J. van Wyk, M.A. van Wyk, and J.J. Botha, A Matching Framework Based on Joint Probabilities Proc. 14th Ann. Symp. Pattern Recognition Assoc. of South Africa, pp. 125-130, Nov. 2004.

Index Terms:
Graph matching, subgraph matching, contextual correspondence matching, projection onto convex sets.
Citation:
Barend J. van Wyk, Micha?l A. van Wyk, "A POCS-Based Graph Matching Algorithm," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 11, pp. 1526-1530, Nov. 2004, doi:10.1109/TPAMI.2004.95
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