Abstract
This paper investigates a technique to extend the tree edit distance framework to allow the simultaneous matching of multiple tree structures. This approach extends a previous result that showed the edit distance between two trees is completely determined by the maximum tree obtained from both tree with node removal operations only. In our approach we seek the minimum structure from which we can obtain the original trees with removal operations. This structure has the added advantage that it can be extended to more than two trees and it imposes consistency on node matches throughout the matched trees. Furthermore through this structure we can get a “natural” embedding space of tree structures that can be used to analyze how tree representations vary in our problem domain.
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References
H. G. Barrow and R. M. Burstall, Subgraph isomorphism, matching relational structures and maximal cliques, Inf. Proc. Letter, Vol. 4, pp. 83, 84, 1976.
M. Bartoli et al., Attributed tree homomorphism using association graphs, In ICPR, 2000.
I. M. Bomze, M. Pelillo, and V. Stix, Approximating the maximum weight clique using replicator dynamics, IEEE Trans. on Neural Networks, Vol. 11, 2000.
H. Bunke and G. Allermann, Inexact graph matching for structural pattern recognition, Pattern Recognition Letters, Vol 1, pp. 245–253, 1983.
H. Bunke and A. Kandel, Mean and maximum common subgraph of two graphs, Pattern Recognition Letters, Vol. 21, pp. 163–168, 2000.
W. J. Christmas and J. Kittler, Structural matching in computer vision using probabilistic relaxation, PAMI, Vol. 17, pp. 749–764, 1995.
T. F. Cootes, C. J. Taylor, and D. H. Cooper, Active shape models-their training and application, CVIU, Vol. 61, pp. 38–59, 1995.
M. A. Eshera and K-S Fu, An image understanding system using attributed symbolic representation and inexact graph-matching, PAMI, Vol 8, pp. 604–618, 1986.
L. E. Gibbons et al., Continuous characterizations of the maximum clique problem, Math. Oper. Res., Vol. 22, pp. 754–768, 1997
T. Heap and D. Hogg, Wormholes in shape space: tracking through discontinuous changes in shape, ICCV, pp. 344–349, 1998.
B. B. Kimia, A. R. Tannenbaum, and S. W. Zucker, Shapes, shocks, and deformations I, International Journal of Computer Vision, Vol. 15, pp. 189–224, 1995.
T. Sebastian, P. Klein, and B. Kimia, Recognition of shapes by editing shock graphs, in ICCV, Vol. I, pp. 755–762, 2001.
B. Luo, et al., A probabilistic framework for graph clustering, in CVPR, Vol. I, pp. 912–919, 2001.
M. Pelillo, K. Siddiqi, and S. W. Zucker, Matching hierarchical structures using association graphs, PAMI, Vol. 21, pp. 1105–1120, 1999.
S. Sclaroff and A. P. Pentland, Modal matching for correspondence and recognition, PAMI, Vol. 17, pp. 545–661, 1995.
A. Shokoufandeh, S. J. Dickinson, K. Siddiqi, and S. W. Zucker, Indexing using a spectral encoding of topological structure, in CVPR, 1999.
K. Siddiqi and B. B. Kimia, A shock grammar for recognition, in CVPR, 507–513, 1996.
K. Siddiqi, S. Bouix, A. Tannenbaum, and S. W. Zucker, The hamilton-jacobi skeleton, in ICCV, pp. 828–834, 1999.
K. Siddiqi et al., Shock graphs and shape matching, Int. J. of Comp. Vision, Vol. 35, pp. 13–32, 1999.
K-C Tai, The tree-to-tree correction problem, J. of the ACM, Vol. 26, pp. 422–433, 1979.
A. Torsello and E. R. Hancock, A skeletal measure of 2D shape similarity, Int. Workshop on Visual Form, LNCS 2059, 2001.
A. Torsello and E. R. Hancock, Efficiently computing weighted tree edit distance using relaxation labeling, in EMMCVPR, LNCS 2134, pp. 438–453, 2001
W. H. Tsai and K. S. Fu, Error-correcting isomorphism of attributed relational graphs for pattern analysis, Sys., Man, and Cyber., Vol. 9, pp. 757–768, 1979.
J. T. L. Wang, K. Zhang, and G. Chirn, The approximate graph matching problem, in ICPR, pp. 284–288, 1994.
R. C. Wilson and E. R. Hancock, Structural matching by discrete relaxation, PAMI, 1997.
K. Zhang, A constrained edit distance between unordered labeled trees, Algorithmica, Vol. 15, pp. 205–222, 1996.
K. Zhang and D. Shasha, Simple fast algorithms for the editing distance between trees and related problems, SIAM J. of Comp., Vol. 18, pp. 1245–1262, 1989.
K. Zhang, R. Statman, and D. Shasha, On the editing distance between unorderes labeled trees, Inf. Proc. Letters, Vol. 42, pp. 133–139, 1992.
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Torsello, A., Hancock, E.R. (2002). Matching and Embedding through Edit-Union of Trees. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds) Computer Vision — ECCV 2002. ECCV 2002. Lecture Notes in Computer Science, vol 2352. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47977-5_54
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DOI: https://doi.org/10.1007/3-540-47977-5_54
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