Fast Fréchet queries

  • Authors:
  • Mark De Berg;Atlas F. Cook, IV;Joachim Gudmundsson

  • Affiliations:
  • Department of Computing Science, TU Eindhoven, The Netherlands;Department of Information and Computing Sciences, Utrecht University, The Netherlands;School of Information Technologies, University of Sydney, Australia and NICTA22NICTA is funded by the Australian Governments represented by the Department of Broadband, Communications and the Digi ...

  • Venue:
  • Computational Geometry: Theory and Applications
  • Year:
  • 2013

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Abstract

Inspired by video analysis of team sports, we study the following problem. Let P be a polygonal path in the plane with n vertices. We want to preprocess P into a data structure that can quickly count the number of inclusion-minimal subpaths of P whose Frechet distance to a given query segment Q is at most some threshold value @e. We present a data structure that solves an approximate version of this problem: it counts all subpaths whose Frechet distance is at most @e, but this count may also include subpaths whose Frechet distance is up to (2+32)@e. For any parameter n@?s@?n^2, our data structure can be tuned such that it uses O(spolylogn) storage and has O((n/s)polylogn) query time.