Publication detail

Structuring Digital Plane by Closure Operators Associated with n-ary Relations

Josef Šlapal

Czech title

Strukturování digitální roviny uzávěrovými operacemi asociovanými s n-árními relacemi

English title

Structuring Digital Plane by Closure Operators Associated with n-ary Relations

Type

conference paper

Language

en

Original abstract

We associate a closure operator with every n-ary relation (n > 1 an integer) on a given set. We focus on certain n-ary relations on the digital line Z and study the closure operators on the digital plane Z^2 that are associated with special products of pairs of the relations. These closure operators, which include the Khalimsky topology, are shown to provide well behaved connectedness, so that they may be used as background structures on the digital plane for the study of digital images.

Czech abstract

S každou n-ární relací asociujeme uzávěrový operátor. Zaměřujeme se na jisté n-ární relace na digitální přímce Z a studujeme uzávěrové operátory na digitální rovině Z^2 asiciované se speciálními součiny dvojic těchto relací.

English abstract

We associate a closure operator with every n-ary relation (n > 1 an integer) on a given set. We focus on certain n-ary relations on the digital line Z and study the closure operators on the digital plane Z^2 that are associated with special products of pairs of the relations. These closure operators, which include the Khalimsky topology, are shown to provide well behaved connectedness, so that they may be used as background structures on the digital plane for the study of digital images.

Keywords in Czech

n-ární relace · uzávěrový operátor · digitální rovina · Khalimského topologie · Jordanova věta

Keywords in English

n-ary relation · Closure operator · Digital plane · Khalimsky topology · Jordan curve theorem

Released

20.05.2019

Publisher

Springer

Location

Svýcarsko

ISBN

978-3-030-20804-2

ISSN

0302-9743

Book

Computational Modeling of Objects Presented in Images. Fundamentals, Methods, and Applications

Volume

2017

Number

1

Edition number

10256

Pages from–to

16–22

Pages count

7

BIBTEX


@inproceedings{BUT157116,
  author="Josef {Šlapal},
  title="Structuring Digital Plane by Closure Operators Associated with n-ary Relations",
  booktitle="Computational Modeling of Objects Presented in Images. Fundamentals, Methods, and Applications",
  year="2019",
  volume="2017",
  number="1",
  month="May",
  pages="16--22",
  publisher="Springer",
  address="Svýcarsko",
  isbn="978-3-030-20804-2",
  issn="0302-9743"
}