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.SoCG.2017.31
URN: urn:nbn:de:0030-drops-71900
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7190/
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Chiu, Man-Kwun ; Korman, Matias

High Dimensional Consistent Digital Segments

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LIPIcs-SoCG-2017-31.pdf (0.7 MB)

Abstract

We consider the problem of digitalizing Euclidean line segments from R^d to Z^d. Christ {et al.} (DCG, 2012) showed how to construct a set of {consistent digital segments} (CDS) for d=2: a collection of segments connecting any two points in Z^2 that satisfies the natural extension of the Euclidean axioms to Z^d. In this paper we study the construction of CDSs in higher dimensions.

We show that any total order can be used to create a set of {consistent digital rays} CDR in Z^d (a set of rays emanating from a fixed point p that satisfies the extension of the Euclidean axioms). We fully characterize for which total orders the construction holds and study their Hausdorff distance, which in particular positively answers the question posed by Christ {et al.}.

BibTeX - Entry

@InProceedings{chiu_et_al:LIPIcs:2017:7190,
  author =	{Man-Kwun Chiu and Matias Korman},
  title =	{{High Dimensional Consistent Digital Segments}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{31:1--31:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Boris Aronov and Matthew J. Katz},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7190},
  URN =		{urn:nbn:de:0030-drops-71900},
  doi =		{10.4230/LIPIcs.SoCG.2017.31},
  annote =	{Keywords: Consistent Digital Line Segments, Digital Geometry, Computer Vision}
}

Keywords: Consistent Digital Line Segments, Digital Geometry, Computer Vision
Collection: 33rd International Symposium on Computational Geometry (SoCG 2017)
Issue Date: 2017
Date of publication: 20.06.2017

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