Publication detail

Closure operators associated to ternary relations for structuring the digital plane

ŠLAPAL, J.

Original Title

Closure operators associated to ternary relations for structuring the digital plane

English Title

Closure operators associated to ternary relations for structuring the digital plane

Language

en

Original Abstract

We study closure operators associated to ternary relations. We focus on a certain ternary relation on the digital line Z and discuss the closure operator on the digital plane Z^2 associated to a special product of two copies of the relation. This closure operator is shown to allow for an analogue of the Jordan curve theorem, so that it may be used as a background structure on the digital plane for the study of digital images. An advantage of this closure operator over the Khalimsky topology is shown, too.

English abstract

We study closure operators associated to ternary relations. We focus on a certain ternary relation on the digital line Z and discuss the closure operator on the digital plane Z^2 associated to a special product of two copies of the relation. This closure operator is shown to allow for an analogue of the Jordan curve theorem, so that it may be used as a background structure on the digital plane for the study of digital images. An advantage of this closure operator over the Khalimsky topology is shown, too.

Keywords

Ternary relation, closure operator, digital space, Khalimsky topology, Jordan curve theorem

Released

30.12.2019

Publisher

IEEE

Location

Los Alamitos, CA, USA

Pages from

125

Pages to

128

Pages count

4

URL

Documents

BibTex


@inproceedings{BUT161342,
  author="Josef {Šlapal}",
  title="Closure operators associated to ternary relations for structuring the digital plane",
  annote="We study closure operators associated to ternary relations. We focus on a certain ternary relation on the digital line Z and discuss the closure operator on the digital plane Z^2 associated to a special product of two copies of the relation. This closure operator is shown to allow for an analogue of the Jordan curve theorem, so that it may be used as a background structure on the digital plane for the study of digital images. An advantage of this closure operator over the Khalimsky topology is shown, too.",
  address="IEEE",
  chapter="161342",
  doi="10.1109/ICAMS.NET46018.2018.00029",
  howpublished="online",
  institution="IEEE",
  year="2019",
  month="december",
  pages="125--128",
  publisher="IEEE"
}