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Mapping Polygons to the Grid with Small Hausdorff and Fréchet Distance

Authors: Quirijn W. Bouts, Irina Irina Kostitsyna, Marc van Kreveld, Wouter Meulemans, Willem Sonke, and Kevin Verbeek

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)


Abstract
We show how to represent a simple polygon P by a (pixel-based) grid polygon Q that is simple and whose Hausdorff or Fréchet distance to P is small. For any simple polygon P, a grid polygon exists with constant Hausdorff distance between their boundaries and their interiors. Moreover, we show that with a realistic input assumption we can also realize constant Fréchet distance between the boundaries. We present algorithms accompanying these constructions, heuristics to improve their output while keeping the distance bounds, and experiments to assess the output.

Cite as

Quirijn W. Bouts, Irina Irina Kostitsyna, Marc van Kreveld, Wouter Meulemans, Willem Sonke, and Kevin Verbeek. Mapping Polygons to the Grid with Small Hausdorff and Fréchet Distance. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 22:1-22:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{bouts_et_al:LIPIcs.ESA.2016.22,
  author =	{Bouts, Quirijn W. and Irina Kostitsyna, Irina and van Kreveld, Marc and Meulemans, Wouter and Sonke, Willem and Verbeek, Kevin},
  title =	{{Mapping Polygons to the Grid with Small Hausdorff and Fr\'{e}chet Distance}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{22:1--22:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.22},
  URN =		{urn:nbn:de:0030-drops-63738},
  doi =		{10.4230/LIPIcs.ESA.2016.22},
  annote =	{Keywords: grid mapping, Hausdorff distance, Fr\'{e}chet distance, digital geometry}
}
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