Graph edit distance from spectral seriation

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 27, Issue 3, 2005, Pages 365-378

  Robles Kelly, Antonio ^a   Hancock, Edwin R ^b  

^a CSIRO   (Australia)

^b UNIVERSITY OF YORK   (United Kingdom)

Author keywords

Graph edit distance; Graph seriation; Graph spectral methods; Maximum a posteriori probability (MAP)

Indexed keywords

COMPUTER GRAPHICS; EIGENVALUES AND EIGENFUNCTIONS; GRAPH THEORY; GRAPHIC METHODS; MATHEMATICAL MODELS; MATRIX ALGEBRA; OBJECT RECOGNITION; PATTERN RECOGNITION; PROBABILITY;

GRAPH EDIT DISTANCE; GRAPH MATCHING; GRAPH SERIATION; GRAPH-SPECTRAL METHODS; MAXIMUM A POSTERIORI PROBABILITY (MAP);

PATTERN MATCHING;

ALGORITHM; ARTICLE; ARTIFICIAL INTELLIGENCE; AUTOMATED PATTERN RECOGNITION; CLUSTER ANALYSIS; COMPARATIVE STUDY; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; EVALUATION; IMAGE ENHANCEMENT; INFORMATION RETRIEVAL; METHODOLOGY; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY;

ALGORITHMS; ARTIFICIAL INTELLIGENCE; CLUSTER ANALYSIS; COMPUTER SIMULATION; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; INFORMATION STORAGE AND RETRIEVAL; PATTERN RECOGNITION, AUTOMATED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY;

EID: 15044365894     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2005.56     Document Type: Article

References (45)

1. J.E. Atkins, E.G. Bowman, and B. Hendrickson, "A Spectral Algorithm for Seriation and the Consecutive Ones Problem," SIAM J. Computing, vol. 28, no. 1, pp. 297-310, 1998.
2. A.D. Bagdanov and M. Worring, "First Order Gaussian Graphs for Efficient Structure Classification," Pattern Recognition, vol. 36, no. 6, pp. 1311-1324, 2003.
3. H. Bunke, "On a Relation between Graph Edit Distance and Maximum Common Subgraph," Pattern Recognition Letters, vol. 18, no. 8, pp. 689-694, 1997.
4. H. Bunke, A. Munger, and X. Jiang, "Combinatorial Search vs. Genetic Algorithms: A Case Study Based on the Generalized Median Graph Problem," Pattern Recognition Letters, vol. 20, nos. 11-13, pp. 1271-1279, 1999.
5. J. Canny, "A Computational Approach to Edge Detection," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 8, no. 6, pp. 679-698, Nov. 1986.
6. 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.
7. F.R.K. Chung, Spectral Graph Theory. Am. Math. Soc., 1997.
8. E.W. Dijkstra, "A Note on Two Problems in Connection with Graphs," Numerische Math, vol. 1, pp. 269-271, 1959.
9. C. Dorai and A.K. Jain, "Shape Spectrum-Based View Grouping and Matching of 3D Free-Form Objects," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 10, pp. 1139-1145, Oct. 1997.
10. M.A. Eshera and K.S. Fu, "A Graph Distance Measure for Image Analysis," IEEE Trans. Systems, Man, and Cybernetics, vol. 14, pp. 398-407, 1984.
11. A.M. Finch, R.C. Wilson, and E.R. Hancock, "An Energy Function and Continuous Edit Process for Graph Matching," Neural Computation, vol. 10, no. 7, pp. 1873-1894, 1998.
12. 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.
13. G.H. Golub and C.F. Van Loan, Matrix Computations. The Johns Hopkins Press, 1996.
14. T. Hofmann and M. Buhmann, "Pairwise Data Clustering by Deterministic Annealing," IEEE Trans. Pattern Analysis and Machine Intelligence vol. 19, no. 1, pp. 1-14, Jan. 1997.
15. R. Horaud and H. Sossa, "Polyhedral Object Recognition by Indexing," Pattern Recognition, vol. 28, no. 12, pp. 1855-1870, 1995.
16. B. Huet and E.R. Hancock, "Relational Object Recognition from Large Structural Libraries," Pattern Recognition, vol. 35, no. 9, pp. 1895-1915, 2002.
17. J. Keuchel, C. Schnorr, C. Schellewald, and D. Cremers, "Binary Partitioning, Perceptual Grouping, and Restoration with Semi-definite Programming," IEEE Trans. Pattern Analysis and Machine Intelligence vol. 25, no. 11, pp. 1364-1379, Nov. 2003.
18. J.J. Koenderink and A.J. van Doorn, "Surface Shape and Curvature Scales," Image and Vision Computing, vol. 10, no. 8, pp. 557-565, 1992.
19. V.I. Levenshtein, "Binary Codes Capable of Correcting Deletions, Insertions, and Reversals," Soviet Physics Doklady, vol. 6, pp. 707-710, 1966.
20. L. Lovasz, "Random Walks on Graphs: A Survey," Bolyai Soc. Math. Studies, vol. 2, no. 2, pp. 1-46, 1993.
21. Bin Luo, A.D.J. Cross, and E.R. Hancock, "Corner Detection via Topographic Analysis of Vector-Potential," Pattern Recognition Letters, vol. 20, no. 6, pp. 635-650, 1999.
22. B. Luo and E.R. Hancock, "Structural Graph Matching Using the EM Algorithm and Singular Value Decomposition," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 10, pp. 1120-1136, Oct. 2001.
23. B. Luo, R.C. Wilson, and E.R. Hancock, "Spectral Embedding of Graphs," Pattern Recognition, vol. 36, pp. 2213-2230, 2003.
24. K.V. Mardia and P.E. Jupp, Directional Statistics. John Wiley & Sons, 2000.
25. B. Mohar, "Some Applications of Laplace Eigenvalues of Graphs," Graph Symmetry: Algebraic Methods and Applications, NATO ASI Series C, G. Hahn and G. Sabidussi, eds., pp. 227-275, 1997.
26. R. Myers, R.C. Wilson, and E.R. Hancock, "Bayesian Graph Edit Distance," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 6, pp. 628-635, June 2000.
27. Y. Peng-Yeng, "Algorithms for Straight Line Fitting Using K-Means," Pattern Recognition Letters, vol. 19, pp. 31-41, 1998.
28. A. Robles-Kelly and E.R. Hancock, "A Probabilistic Spectral Framework for Spectral Clustering and Grouping," Pattern Recognition, vol. 37, no. 7, pp. 1387-1405, 2004.
29. A. Robles-Kelly and E.R. Hancock, "String Edit Distance, Random Walks and Graph Matching," Int'l J. Pattern Recognition and Artificial Intelligence, vol. 18, no. 3, pp. 315-327, 2004.
30. A. Robles-Kelly, S. Sarkar, and E.R. Hancock, "A Fast Leading Eigenvector Approximation for Segmentation and Grouping," Proc. Int'l Conf. Pattern Recognition, pp. 639-642, 2002.
31. A. Sanfeliu and K.S. Fu, "A Distance Measure between Attributed Relational Graphs for Pattern Recognition," IEEE Trans. Systems, Man, and Cybernetics, vol. 13, no. 353-362, 1983.
32. G. Scott and H. Longuet-Higgins, "An Algorithm for Associating the Features of Two Images," Proc. Royal Soc. London, no. 244 in B, pp. 21-26, 1991.
33. B. Selman, H.A. Kautz, and B. Cohen, "Noise Strategies for Improving Local Search," Proc. 12th Nat'l Conf. Artificial Intelligence, pp. 337-343, 1994.
34. L.G. Shapiro and R.M. Haralick, "Relational Models for Scene Analysis," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 4, pp. 595-602, 1982.
35. L.S. Shapiro and J.M. Brady, "A Modal Approach to Feature-Based Correspondence," Proc. British Machine Vision Conf., pp. 78-85, 1991.
36. A. Shokoufandeh, S.J. Dickinson, K. Siddiqi, and S.W. Zucker, "Indexing Using a Spectral Encoding of Topological Structure," Proc. Computer Vision and Pattern Recognition, pp. 491-497, 1998.
37. O. Steinmann, A. Strohmaier, and T. Stutzle, "Tabu Search vs. Random Walk," Proc. Advances in Artificial Intelligence (KI '97), pp. 337-348, 1997.
38. G.W. Stewart and J.-G. Sun, Matrix Perturbation Theory. Academic Press, 1990.
39. M. Tuceryan and T. Chorzempa, "Relative Sensitivity of a Family of Closest-Point Graphs in Computer Vision Applications," Pattern Recognition, vol. 24, no. 5, pp. 361-373, 1991.
40. S. Umeyama, "An Eigen Decomposition Approach to Weighted Graph Matching Problems," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 10, no. 5, pp. 695-703, Sept. 1988.
41. R.S. Varga, Matrix Iterative Analysis, second ed. Springer, 2000.
42. R.A. Wagner and M.J. Fisher, "The String-to-String Correction Problem," J. ACM, vol. 21, no. 1, pp. 168-173, 1974.
43. R.C. Wilson and E.R. Hancock, "A Bayesian Compatibility Model for Graph Matching," Pattern Recognition Letters, vol. 17, pp. 263-276, 1996.
44. R.C. Wilson and E.R. Hancock, "Structural Matching by Discrete Relaxation," IEEE Trans. Pattern Analysis and Machine Intelligence vol. 19, no. 6, pp. 634-648, June 1997.
45. P.L. Worthington and E.R. Hancock, "New Constraints on Data-Closeness and Needle Map Consistency for Shape-From-Shading," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 12, pp. 1250-1267, Dec. 1999.