Publication result detail

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

Josef Šlapal

Original Title

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

English Title

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

Type

Paper in proceedings (conference paper)

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.

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

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

Key words in English

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

Authors

Josef Šlapal

RIV year

2020

Released

20.05.2019

Publisher

Springer

Location

Svýcarsko

ISBN

978-3-030-20804-2

Book

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

Edition

Lecture Notes in Computer Science

ISBN

0302-9743

Periodical

Lecture Notes in Computer Science

Volume

2017

Number

1

State

Federal Republic of Germany

Pages from

16

Pages to

22

Pages count

7

URL

https://link.springer.com/chapter/10.1007/978-3-030-20805-9_2

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",
  series="Lecture Notes in Computer Science",
  journal="Lecture Notes in Computer Science",
  volume="2017",
  number="1",
  pages="16--22",
  publisher="Springer",
  address="Svýcarsko",
  doi="10.1007/978-3-030-20805-9\{_}2",
  isbn="978-3-030-20804-2",
  issn="0302-9743",
  url="https://link.springer.com/chapter/10.1007/978-3-030-20805-9_2"
}