Computing the similarity between moving curves

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In this paper we study similarity measures for moving curves which can, for example, model changing coastlines or retreating glacier termini. Points on a moving curve have two parameters, namely the position along the curve as well as time. We therefore focus on similarity measures for surfaces, specifically the Fréchet distance between surfaces. While the Fréchet distance between surfaces is generally NP-hard, we show for variants arising in the context of moving curves that they are polynomial-time solvable or NP-complete depending on the restrictions imposed on how the moving curves are matched. We achieve the polynomial-time solutions by a novel approach for computing a surface in the so-called free-space diagram based on a relation between obstacles.

Original languageEnglish
Pages (from-to)2-14
Number of pages13
JournalComputational Geometry
Early online date17 Jan 2017
Publication statusPublished - Aug 2018


  • Complex moving objects
  • Distance between surfaces
  • Fréchet distance
  • Moving curves


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