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Uncertain Curve Simplification

Authors Kevin Buchin , Maarten Löffler, Aleksandr Popov , Marcel Roeloffzen



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Author Details

Kevin Buchin
  • Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands
Maarten Löffler
  • Department of Information and Computing Sciences, Utrecht University, The Netherlands
Aleksandr Popov
  • Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands
Marcel Roeloffzen
  • Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands

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Kevin Buchin, Maarten Löffler, Aleksandr Popov, and Marcel Roeloffzen. Uncertain Curve Simplification. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 26:1-26:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.MFCS.2021.26

Abstract

We study the problem of polygonal curve simplification under uncertainty, where instead of a sequence of exact points, each uncertain point is represented by a region which contains the (unknown) true location of the vertex. The regions we consider are disks, line segments, convex polygons, and discrete sets of points. We are interested in finding the shortest subsequence of uncertain points such that no matter what the true location of each uncertain point is, the resulting polygonal curve is a valid simplification of the original polygonal curve under the Hausdorff or the Fréchet distance. For both these distance measures, we present polynomial-time algorithms for this problem.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Curves
  • Uncertainty
  • Simplification
  • Fréchet Distance
  • Hausdorff Distance

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