Publication result detail

Digital Jordan Curves and Surfaces with Respect to a Closure Operator

ŠLAPAL, J.

Original Title

Digital Jordan Curves and Surfaces with Respect to a Closure Operator

English Title

Digital Jordan Curves and Surfaces with Respect to a Closure Operator

Type

WoS Article

Original Abstract

In this paper, we propose new definitions of digital Jordan curves and digital Jordan surfaces. We start with introducing and studying closure operators on a given set that are associated with n-ary relations (n > 1 an integer) on this set. Discussed are in particular the closure operators associated with certain n-ary relations on the digital line Z. Of these relations, we focus on a ternary one equipping the digital plane Z(2) and the digital space Z(3) with the closure operator associated with the direct product of two and three, respectively, copies of this ternary relation. The connectedness provided by the closure operator is shown to be suitable for defining digital curves satisfying a digital Jordan curve theorem and digital surfaces satisfying a digital Jordan surface theorem.

English abstract

In this paper, we propose new definitions of digital Jordan curves and digital Jordan surfaces. We start with introducing and studying closure operators on a given set that are associated with n-ary relations (n > 1 an integer) on this set. Discussed are in particular the closure operators associated with certain n-ary relations on the digital line Z. Of these relations, we focus on a ternary one equipping the digital plane Z(2) and the digital space Z(3) with the closure operator associated with the direct product of two and three, respectively, copies of this ternary relation. The connectedness provided by the closure operator is shown to be suitable for defining digital curves satisfying a digital Jordan curve theorem and digital surfaces satisfying a digital Jordan surface theorem.

Keywords

Digital space; n-ary relation; closure operator; connectedness; digital Jordan curve; digital Jordan surface

Key words in English

Digital space; n-ary relation; closure operator; connectedness; digital Jordan curve; digital Jordan surface

Authors

ŠLAPAL, J.

RIV year

2021

Released

21.03.2021

Publisher

IOS PRESS

Location

AMSTERDAM

ISBN

0169-2968

Periodical

FUNDAMENTA INFORMATICAE

Volume

179

Number

1

State

Republic of Poland

Pages from

59

Pages to

74

Pages count

16

URL

https://content.iospress.com/articles/fundamenta-informaticae/fi2013

BibTex

@article{BUT168052,
  author="Josef {Šlapal}",
  title="Digital Jordan Curves and Surfaces with Respect to a Closure Operator",
  journal="FUNDAMENTA INFORMATICAE",
  year="2021",
  volume="179",
  number="1",
  pages="59--74",
  doi="10.3233/FI-2021-2013",
  issn="0169-2968",
  url="https://content.iospress.com/articles/fundamenta-informaticae/fi2013"
}