Detail výsledku

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. no. 01012, p. 1-5. ISSN: 2271-2097.
Typ
článek ve sborníku konference
Jazyk
anglicky
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Abstrakt

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.

 

Klíčová slova

Ternary relation, connectedness, digital plane, Jordan curve theorem

Rok
2017
Strany
1–5
Časopis
ITM Web of Conferences, roč. 9, č. 01012, ISSN 2271-2097
Sborník
AMCSE 2016
Konference
International Conference Applied Mathematics, Computational Science and Systems Engineering
Vydavatel
EDP Sciences
Místo
Les Ulis Cedex A
DOI
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/"
}
Soubory
Projekty
IT4Innovations excellence in science, MŠMT, Národní program udržitelnosti II, LQ1602, zahájení: 2016-01-01, ukončení: 2020-12-31, ukončen
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