Abstract
Given a set of polygonal curves we seek to find a middle curve that represents the set of curves. We require that the middle curve consists of points of the input curves and that it minimizes the discrete Fréchet distance to the input curves. We present algorithms for three different variants of this problem: computing an ordered middle curve, computing an ordered and restricted middle curve, and computing an unordered middle curve.
This work was partially supported by research grant AL 253/8-1 from Deutsche Forschungsgemeinschaft (German Science Association), and by the National Science Foundation under grant CCF-1301911. Work by Ahn and Oh was supported by the NRF grant 2011-0030044 (SRC-GAIA) funded by the government of Korea.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alt, H., Godau, M.: Computing the Fréchet distance between two polygonal curves. Int. J. Comput. Geom. Appl. 5, 75–91 (1995)
Buchin, K., Buchin, M., Gudmundsson, J., Löffler, M., Luo, J.: Detecting commuting patterns by clustering subtrajectories. In: Hong, S.-H., Nagamochi, H., Fukunaga, T. (eds.) ISAAC 2008. LNCS, vol. 5369, pp. 644–655. Springer, Heidelberg (2008)
Buchin, K., Buchin, M., van Kreveld, M., Löffler, M., Silveira, R.I., Wenk, C., Wiratma, L.: Median trajectories. Algorithmica 66(3), 595–614 (2013)
Dumitrescu, A., Rote, G.: On the Fréchet distance of a set of curves. In: Proceedings of the 16th Canadian Conference on Computational Geometry, CCCG 2004, Concordia University, Montréal, Québec, Canada, pp. 162–165, 9–11 August 2004
Eiter, T., Mannila, H.: Computing discrete Fréchet distance. Technical report, Technische Universität Wien (1994)
Har-Peled, S., Raichel, B.: The Fréchet distance revisited and extended. ACM Trans. Algorithms 10(1), 3:1–3:22 (2014)
Sriraghavendra, E., Karthik, K., Bhattacharyya, C.: Fréchet distance based approach for searching online handwritten documents. In: Proceedings of the Ninth International Conference on Document Analysis and Recognition, ICDAR 2007, vol. 1, pp. 461–465. IEEE Computer Society (2007)
van Kreveld, M.J., Löffler, M., Staals, F.: Central trajectories. In: 31st European Workshop on Computational Geometry (EuroCG), Book of Abstracts, pp. 129–132 (2015)
Zhu, H., Luo, J., Yin, H., Zhou, X., Huang, J.Z., Zhan, F.B.: Mining trajectory corridors using Fréchet distance and meshing grids. In: Zaki, M.J., Yu, J.X., Ravindran, B., Pudi, V. (eds.) PAKDD 2010, Part I. LNCS, vol. 6118, pp. 228–237. Springer, Heidelberg (2010)
Acknowledgments
This work was initiated at the 17th Korean Workshop on Computational Geometry. We thank the organizers and all participants for the stimulating atmosphere. In particular we thank Fabian Stehn and Wolfgang Mulzer for discussing this paper.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ahn, HK., Alt, H., Buchin, M., Oh, E., Scharf, L., Wenk, C. (2016). A Middle Curve Based on Discrete Fréchet Distance. In: Kranakis, E., Navarro, G., Chávez, E. (eds) LATIN 2016: Theoretical Informatics. LATIN 2016. Lecture Notes in Computer Science(), vol 9644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49529-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-662-49529-2_2
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-49528-5
Online ISBN: 978-3-662-49529-2
eBook Packages: Computer ScienceComputer Science (R0)