Publication detail

Digital Jordan Curves and Surfaces with Respect to a Closure Operator

ŠLAPAL, J.

English title

Digital Jordan Curves and Surfaces with Respect to a Closure Operator

Type

journal article in Web of Science

Language

en

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 in English

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

Released

21.03.2021

Publisher

IOS PRESS

Location

AMSTERDAM

ISSN

0169-2968

Volume

179

Number

1

Pages from–to

59–74

Pages count

16

BIBTEX


@article{BUT168052,
  author="Josef {Šlapal},
  title="Digital Jordan Curves and Surfaces with Respect to a Closure Operator",
  year="2021",
  volume="179",
  number="1",
  month="March",
  pages="59--74",
  publisher="IOS PRESS",
  address="AMSTERDAM",
  issn="0169-2968"
}