Computing the Fréchet Distance between Folded Polygons

  • Atlas F. CookIV
  • Anne Driemel
  • Sariel Har-Peled
  • Jessica Sherette
  • Carola Wenk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6844)

Abstract

Computing the Fréchet distance for surfaces is a surprisingly hard problem and the only known algorithm is limited to computing it between flat surfaces. We adapt this algorithm to create one for computing the Fréchet distance for a class of non-flat surfaces which we call folded polygons. Unfortunately, the original algorithm cannot be extended directly. We present three different methods to adapt it. The first of which is a fixed-parameter tractable algorithm. The second is a polynomial-time approximation algorithm. Finally, we present a restricted class of folded polygons for which we can compute the Fréchet distance in polynomial time.

Keywords

Computational Geometry Shape Matching Fréchet Distance 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Atlas F. CookIV
    • 1
  • Anne Driemel
    • 1
  • Sariel Har-Peled
    • 2
  • Jessica Sherette
    • 3
  • Carola Wenk
    • 3
  1. 1.Department of Information and Computing SciencesUniversity of UtrechtNetherlands
  2. 2.Department of Computer ScienceUniversity of IllinoisUSA
  3. 3.Department of Computer ScienceUniversity of TexasSan AntonioUSA

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