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Partial Matching between Surfaces Using Fréchet Distance

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7357)

Abstract

Computing the Fréchet distance for surfaces is a surprisingly hard problem. We introduce a partial variant of the Fréchet distance problem, which for given surfaces P and Q asks to compute a surface R ⊆ Q with minimum Fréchet distance to P. Like the Fréchet distance, the partial Fréchet distance is NP-hard to compute between terrains and also between polygons with holes. We restrict P, Q, and R to be coplanar simple polygons. For this restricted class of surfaces, we develop a polynomial time algorithm to compute the partial Fréchet distance and show that such an R ⊆ Q can be computed in polynomial time as well. This is the first algorithm to address a partial Fréchet distance problem for surfaces and extends Buchin et al.’s algorithm for computing the Fréchet distance between simple polygons.

Keywords

  • Computational Geometry
  • Shape Matching
  • Fréchet Distance

This work has been supported by the National Science Foundation grant NSF CAREER CCF-0643597.

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Sherette, J., Wenk, C. (2012). Partial Matching between Surfaces Using Fréchet Distance. In: Fomin, F.V., Kaski, P. (eds) Algorithm Theory – SWAT 2012. SWAT 2012. Lecture Notes in Computer Science, vol 7357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31155-0_2

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  • DOI: https://doi.org/10.1007/978-3-642-31155-0_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31154-3

  • Online ISBN: 978-3-642-31155-0

  • eBook Packages: Computer ScienceComputer Science (R0)