Publication detail

Relation-induced connectedness in the digital plane

ŠLAPAL, J.

Original Title

Relation-induced connectedness in the digital plane

Type

journal article in Web of Science

Language

English

Original Abstract

We introduce and discuss a connectedness induced by n-ary relations (n > 1 an integer) on their underlying sets. In particular, we focus on certain n-ary relations with the induced connectedness allowing for a definition of digital Jordan curves. For every integer n > 1, we introduce one such n-ary relation on the digital plane Z2 and prove a digital analogue of the Jordan curve theorem for the induced connectedness. It follows that these n-ary relations may be used as convenient structures on the digital plane for the study of geometric properties of digital images. For n = 2, such a structure coincides with the (specialization order of the) Khalimsky topology and, for n > 2, it allows for a variety of Jordan curves richer than that provided by the Khalimsky topology.

Keywords

n-Ary relation, Connectedness, Digital plane, Khalimsky topology, Jordan curve

Authors

ŠLAPAL, J.

Released

10. 1. 2018

ISBN

0001-9054

Periodical

AEQUATIONES MATHEMATICAE

Year of study

2018

Number

95

State

Swiss Confederation

Pages from

75

Pages to

90

Pages count

16

URL

https://www.fit.vut.cz/research/publication/11754/

BibTex

@article{BUT143013,
  author="Josef {Šlapal}",
  title="Relation-induced connectedness in the digital plane",
  journal="AEQUATIONES MATHEMATICAE",
  year="2018",
  volume="2018",
  number="95",
  pages="75--90",
  doi="10.1007/s00010-017-0508-5",
  issn="0001-9054",
  url="https://www.fit.vut.cz/research/publication/11754/"
}