@inproceedings{ed967a55bd4b45ec8617ff917e7de57f,
title = "High dimensional consistent digital segments",
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.",
keywords = "Computer vision, Consistent digital line segments, Digital geometry",
author = "Chiu, {Man Kwun} and Matias Korman",
year = "2017",
month = jun,
day = "1",
doi = "10.4230/LIPIcs.SoCG.2017.31",
language = "English",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
publisher = "Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing",
pages = "311--3115",
editor = "Katz, {Matthew J.} and Boris Aronov",
booktitle = "33rd International Symposium on Computational Geometry, SoCG 2017",
note = "33rd International Symposium on Computational Geometry, SoCG 2017 ; Conference date: 04-07-2017 Through 07-07-2017",
}