License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2016.27
URN: urn:nbn:de:0030-drops-63783
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Chambers, Erin ; Kostitsyna, Irina ; Löffler, Maarten ; Staals, Frank

Homotopy Measures for Representative Trajectories

LIPIcs-ESA-2016-27.pdf (1 MB)


An important task in trajectory analysis is defining a meaningful representative for a cluster of similar trajectories. Formally defining and computing such a representative r is a challenging problem. We propose and discuss two new definitions, both of which use only the geometry of the input trajectories. The definitions are based on the homotopy area as a measure of similarity between two curves, which is a minimum area swept by all possible deformations of one curve into the other. In the first definition we wish to minimize the maximum homotopy area between r and any input trajectory, whereas in the second definition we wish to minimize the sum of the homotopy areas between r and the input trajectories. For both definitions computing an optimal representative is NP-hard. However, for the case of minimizing the sum of the homotopy areas, an optimal representative can be found efficiently in a natural class of restricted inputs, namely, when the arrangement of trajectories forms a directed acyclic graph.

BibTeX - Entry

  author =	{Erin Chambers and Irina Kostitsyna and Maarten L{\"o}ffler and Frank Staals},
  title =	{{Homotopy Measures for Representative Trajectories}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{27:1--27:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Piotr Sankowski and Christos Zaroliagis},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-63783},
  doi =		{10.4230/LIPIcs.ESA.2016.27},
  annote =	{Keywords: trajectory analysis, representative trajectory, homotopy area}

Keywords: trajectory analysis, representative trajectory, homotopy area
Collection: 24th Annual European Symposium on Algorithms (ESA 2016)
Issue Date: 2016
Date of publication: 18.08.2016

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