Abstract
The Fréchet distance is a metric to compare two curves, which is based on monotonous matchings between these curves. We call a matching that results in the Fréchet distance a Fréchet matching. There are often many different Fréchet matchings and not all of these capture the similarity between the curves well. We propose to restrict the set of Fréchet matchings to “natural” matchings and to this end introduce locally correct Fréchet matchings. We prove that at least one such matching exists for two polygonal curves and give an O(N 3 logN) algorithm to compute it, where N is the total number of edges in both curves. We also present an O(N 2) algorithm to compute a locally correct discrete Fréchet matching.
M. Buchin is supported by the Netherlands Organisation for Scientific Research (NWO) under project no. 612.001.106. W. Meulemans and B. Speckmann are supported by the Netherlands Organisation for Scientific Research (NWO) under project no. 639.022.707. A short abstract of the results presented in Section 3 and Section 4 appeared at the informal workshop EuroCG 2012. For omitted proofs we refer to [4].
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References
Alt, H., Godau, M.: Computing the Fréchet distance between two polygonal curves. Int. J. of Comp. Geometry and Appl. 5(1), 75–91 (1995)
Buchin, K., Buchin, M., Gudmundsson, J.: Constrained free space diagrams: a tool for trajectory analysis. Int. J. of GIS 24(7), 1101–1125 (2010)
Buchin, K., Buchin, M., Gudmundsson, J., Löffler, M., Luo, J.: Detecting Commuting Patterns by Clustering Subtrajectories. Int. J. of Comp. Geometry and Appl. 21(3), 253–282 (2011)
Buchin, K., Buchin, M., Meulemans, W., Speckmann, B.: Locally correct Fre ́chet matchings. CoRR, abs/1206.6257 (June 2012)
Efrat, A., Guibas, L., Har-Peled, S., Mitchell, J., Murali, T.: New Similarity Measures between Polylines with Applications to Morphing and Polygon Sweeping. Discrete & Comp. Geometry 28(4), 535–569 (2002)
Eiter, T., Mannila, H.: Computing Discrete Fréchet Distance. Technical Report CD-TR 94/65, Christian Doppler Laboratory (1994)
Har-Peled, S., Raichel, B.: Fre ́chet distance revisited and extended. CoRR, abs/1202.5610 (February 2012)
Maheshwari, A., Sack, J., Shahbaz, K., Zarrabi-Zadeh, H.: Fréchet distance with speed limits. Comp. Geometry: Theory and Appl. 44(2), 110–120 (2011)
Wenk, C., Salas, R., Pfoser, D.: Addressing the need for map-matching speed: Localizing global curve-matching algorithms. In: Proc. 18th Int. Conf. on Sci. and Stat. Database Management, pp. 379–388 (2006)
Wylie, T., Zhu, B.: A Polynomial Time Solution for Protein Chain Pair Simplification under the Discrete Fréchet Distance. In: Bleris, L., Măndoiu, I., Schwartz, R., Wang, J. (eds.) ISBRA 2012. LNCS, vol. 7292, pp. 287–298. Springer, Heidelberg (2012)
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Buchin, K., Buchin, M., Meulemans, W., Speckmann, B. (2012). Locally Correct Fréchet Matchings. In: Epstein, L., Ferragina, P. (eds) Algorithms – ESA 2012. ESA 2012. Lecture Notes in Computer Science, vol 7501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33090-2_21
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DOI: https://doi.org/10.1007/978-3-642-33090-2_21
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