Publication Details

A ternary relation for structuring the digital plane

ŠLAPAL, J. A ternary relation for structuring the digital plane. In AMCSE 2016. ITM Web of Conferences. Les Ulis Cedex A: EDP Sciences, 2017. p. 1-5. ISSN: 2271-2097.
Czech title
Ternární relace pro strukturování digitální roviny
Type
conference paper
Language
English
Authors
Šlapal Josef, prof. RNDr., CSc. (IM DAAG)
Keywords

Ternary relation, connectedness, digital plane, Jordan curve theorem

Abstract

We discuss certain ternary relations, called plain, and show that each of them induces a connectedness on its underlying set. This connectedness allows for definitions of concepts of simple closed and Jordan curves. We introduce a particular plain ternary relation on the digital plane Z^2 and, as the main result, we prove a digital analogue of the Jordan curve theorem for the connectedness induced by this relation. It follows that the ternary relation introduced may be used as a convenient structure on the digital plane for the study of the geometric properties of digital images that are related to boundaries because boundaries of objects in digital images are represented by digital Jordan curves. An advantage of this structure over the Khalimsky topology is that it allows Jordan curves to turn at the acute angle /4 at some points.  

Published
2017
Pages
1–5
Journal
ITM Web of Conferences, vol. 9, no. 01012, ISSN 2271-2097
Proceedings
AMCSE 2016
Publisher
EDP Sciences
Place
Les Ulis Cedex A
DOI
10.1051/itmconf/20170901012
UT WoS
000402753800012
BibTeX 
@inproceedings{BUT144501,
  author="Josef {Šlapal}",
  title="A ternary relation for structuring the digital plane",
  booktitle="AMCSE 2016",
  year="2017",
  journal="ITM Web of Conferences",
  volume="9",
  number="01012",
  pages="1--5",
  publisher="EDP Sciences",
  address="Les Ulis Cedex A",
  doi="10.1051/itmconf/20170901012",
  issn="2271-2097",
  url="https://www.fit.vut.cz/research/publication/11594/"
}
Files
Back to top