Abstract
Graph edit distance is a powerful error-tolerant similarity measure for graphs. For pattern recognition problems involving large graphs, however, the high computational complexity makes it sometimes impossible to apply edit distance algorithms. In the present paper we propose an efficient algorithm for edit distance computation of planar graphs. Given graphs embedded in the plane, we iteratively match small subgraphs by locally optimizing structural correspondences. Eventually we obtain a valid edit path and hence an upper bound of the edit distance. To demonstrate the efficiency of our approach, we apply the proposed algorithm to the problem of fingerprint classification.
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Bunke, H., Shearer, K.: A graph distance metric based on the maximal common subgraph. Pattern Recognition Letters 19, 255–259 (1998)
Fernandez, M.L., Valiente, G.: A graph distance metric combining maximum common subgraph and minimum common supergraph. Pattern Recognition Letters 22, 753–758 (2001)
Wallis, W., Shoubridge, P., Kraetzl, M., Ray, D.: Graph distances using graph union. Pattern Recognition Letters 22, 701–704 (2001)
Sanfeliu, A., Fu, K.: A distance measure between attributed relational graphs for pattern recognition. IEEE Transactions on Systems, Man, and Cybernetics 13, 353–363 (1983)
Messmer, B., Bunke, H.: A new algorithm for error-tolerant subgraph isomorphism detection. IEEE Transactions on Pattern Analysis and Machine Intelligence 20, 493–504 (1998)
Hopcroft, J., Wong, J.: Linear time algorithm for isomorphism of planar graphs. In: Proc. 6th Annual ACM Symposium on Theory of Computing, pp. 172–184 (1974)
Luks, E.: Isomorphism of graphs of bounded valence can be tested in ploynomial time. Journal of Computer and Systems Sciences 25, 42–65 (1982)
Dickinson, P., Bunke, H., Dadej, A., Kraetzl, M.: On graphs with unique node labels. In: Hancock, E.R., Vento, M. (eds.) GbRPR 2003. LNCS, vol. 2726, pp. 13–23. Springer, Heidelberg (2003)
Lumini, A., Maio, D., Maltoni, D.: Inexact graph matching for fingerprint classification. Machine Graphics and Vision, Special Issue on Graph Transformations in Pattern Generation and CAD 8, 231–248 (1999)
Ambauen, R., Fischer, S., Bunke, H.: Graph edit distance with node splitting and merging and its application to diatom identification. In: Hancock, E.R., Vento, M. (eds.) GbRPR 2003. LNCS, vol. 2726, pp. 95–106. Springer, Heidelberg (2003)
Bunke, H., Bühler, U.: Applications of approximate string matching to 2D shape recognition. Pattern Recognition 26, 1797–1812 (1993)
Lladós, J., MartÃ, E., Villanueva, J.: Symbol recognition by error-tolerant subgraph matching between region adjacency graphs. IEEE Transactions on Pattern Analysis and Machine Intelligence 23, 1137–1143 (2001)
Peris, G., Marzal, A.: Fast cyclic edit distance computation with weighted edit costs in classification. In: Kasturi, R., Laurendeau, D., Suen, C. (eds.) Proc. 16th Int. Conf. on Pattern Recognition, vol. 4, pp. 184–187 (2002)
Mollineda, R., Vidal, E., Casacuberta, F.: A windowed weighted approach for approximate cyclic string matching. In: Kasturi, R., Laurendeau, D., Suen, C. (eds.) Proc. 16th Int. Conf. on Pattern Recognition, pp. 188–191 (2002)
Robles-Kelly, A., Hancock, E.: String edit distance, random walks and graph matching. In: Int. Journal of Pattern Recognition and Artificial Intelligence (2004) (to appear)
Kawagoe, M., Tojo, A.: Fingerprint pattern classification. Pattern Recognition 17, 295–303 (1984)
Karu, K., Jain, A.: Fingerprint classification. Pattern Recognition 29, 389–404 (1996)
Rao, K., Balck, K.: Type classification of fingerprints: A syntactic approach. IEEE Transactions on Pattern Analysis and Machine Intelligence 2, 223–231 (1980)
Jain, A., Prabhakar, S., Hong, L.: A multichannel approach to fingerprint classification. IEEE Transactions on Pattern Analysis and Machine Intelligence 21, 348–359 (1999)
Wilson, C., Candela, G., Watson, C.: Neural network fingerprint classification. Journal of Artificial Neural Networks 1, 203–228 (1994)
Marcialis, G., Roli, F., Serrau, A.: Fusion of statistical and structural fingerprint classifiers. In: Kittler, J., Nixon, M.S. (eds.) AVBPA 2003. LNCS, vol. 2688, pp. 310–317. Springer, Heidelberg (2003)
Watson, C., Wilson, C.: NIST Special Database 4. Fingerprint Database (1992)
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Neuhaus, M., Bunke, H. (2004). An Error-Tolerant Approximate Matching Algorithm for Attributed Planar Graphs and Its Application to Fingerprint Classification. 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_18
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DOI: https://doi.org/10.1007/978-3-540-27868-9_18
Publisher Name: Springer, Berlin, Heidelberg
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