High dimensional consistent digital segments

Man Kwun Chiu, Matias Korman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

We consider the problem of digitalizing Euclidean line segments from ℝd to ℤd. 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 ℤ2 that satisfies the natural extension of the Euclidean axioms to ℤd. 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 ℤd (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.

Original languageEnglish
Title of host publication33rd International Symposium on Computational Geometry, SoCG 2017
EditorsMatthew J. Katz, Boris Aronov
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages311-3115
Number of pages2805
ISBN (Electronic)9783959770385
DOIs
Publication statusPublished - 2017 Jun 1
Event33rd International Symposium on Computational Geometry, SoCG 2017 - Brisbane, Australia
Duration: 2017 Jul 42017 Jul 7

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume77
ISSN (Print)1868-8969

Other

Other33rd International Symposium on Computational Geometry, SoCG 2017
CountryAustralia
CityBrisbane
Period17/7/417/7/7

Keywords

  • Computer vision
  • Consistent digital line segments
  • Digital geometry

ASJC Scopus subject areas

  • Software

Cite this

Chiu, M. K., & Korman, M. (2017). High dimensional consistent digital segments. In M. J. Katz, & B. Aronov (Eds.), 33rd International Symposium on Computational Geometry, SoCG 2017 (pp. 311-3115). (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 77). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.SoCG.2017.31