Partial Matching between Surfaces Using Fréchet Distance

  • Jessica Sherette
  • Carola Wenk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jessica Sherette
    • 1
  • Carola Wenk
    • 1
  1. 1.Department of Computer ScienceUniversity of Texas at San AntonioUSA

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