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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, Kevin Verbeek

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Quirijn W. Bouts
Irina Irina Kostitsyna
Marc van Kreveld
Wouter Meulemans
Willem Sonke
Kevin Verbeek

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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)
https://doi.org/10.4230/LIPIcs.ESA.2016.22

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.
Keywords
  • grid mapping
  • Hausdorff distance
  • Fréchet distance
  • digital geometry

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