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A Middle Curve Based on Discrete Fréchet Distance

  • Hee-Kap Ahn
  • Helmut Alt
  • Maike Buchin
  • Eunjin Oh
  • Ludmila Scharf
  • Carola Wenk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9644)

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.

Keywords

Covering Sequence Voronoi Diagram Binary Search Dynamic Programming Algorithm Decision Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

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.

References

  1. 1.
    Alt, H., Godau, M.: Computing the Fréchet distance between two polygonal curves. Int. J. Comput. Geom. Appl. 5, 75–91 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    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)CrossRefGoogle Scholar
  3. 3.
    Buchin, K., Buchin, M., van Kreveld, M., Löffler, M., Silveira, R.I., Wenk, C., Wiratma, L.: Median trajectories. Algorithmica 66(3), 595–614 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    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 2004Google Scholar
  5. 5.
    Eiter, T., Mannila, H.: Computing discrete Fréchet distance. Technical report, Technische Universität Wien (1994)Google Scholar
  6. 6.
    Har-Peled, S., Raichel, B.: The Fréchet distance revisited and extended. ACM Trans. Algorithms 10(1), 3:1–3:22 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    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)Google Scholar
  8. 8.
    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)Google Scholar
  9. 9.
    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)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Hee-Kap Ahn
    • 1
  • Helmut Alt
    • 2
  • Maike Buchin
    • 3
  • Eunjin Oh
    • 1
  • Ludmila Scharf
    • 2
  • Carola Wenk
    • 4
  1. 1.Pohang University of Science and TechnologyPohangKorea
  2. 2.Free University of BerlinBerlinGermany
  3. 3.Ruhr University BochumBochumGermany
  4. 4.Tulane UniversityNew OrleansUSA

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