Publication detail

Alexandroff pretopologies for structuring the digital plane

ŠLAPAL, J.

Original Title

Alexandroff pretopologies for structuring the digital plane

Type

journal article in Web of Science

Language

English

Original Abstract

We explore the possibility of employing Alexandroff pretopologies as structures on the digital plane Z^2 convenient for the study of geometric and topological properties of digital images. These pretopologies are known to be in one-to-one correspondence with reflexive binary relations so that graph-theoretic methods may be used when investigating them. We discuss such Alexandroff pretopologies on Z2 that possess a rich variety of digital Jordan curves obtained as circuits in a natural graph with the vertex set Z2. Of these pretopologies, we focus on the minimal ones and study their quotient pretopologies on Z2 which are shown to allow for various digital Jordan curve theorems. We also develop a method for identifying Jordan curves in the minimal pretopological spaces by using Jordan curves in one of their quotient spaces. Using this method, we conclude the paper with proving a digital Jordan curve theorem for the minimal pretopologies.

Keywords

Digital plane, Jordan curve, Alexandroff pretopology, quotient pretopology

Authors

ŠLAPAL, J.

Released

15. 1. 2017

Publisher

Elsevier

Location

Nizozemsko

ISBN

0166-218X

Periodical

Discrete Applied Mathematics

Year of study

216

Number

2

State

Kingdom of the Netherlands

Pages from

323

Pages to

334

Pages count

12

URL

https://ac.els-cdn.com/S0166218X16302670/1-s2.0-S0166218X16302670-main.pdf?_tid=b5db0aee-e1e1-11e7-b51a-00000aab0f02&acdnat=1513374708_82e3d74b75420ea8adca800b18dc4e43

BibTex

@article{BUT125480,
  author="Josef {Šlapal}",
  title="Alexandroff pretopologies for structuring the digital plane",
  journal="Discrete Applied Mathematics",
  year="2017",
  volume="216",
  number="2",
  pages="323--334",
  doi="10.1016/j.dam.2016.06.002",
  issn="0166-218X",
  url="https://ac.els-cdn.com/S0166218X16302670/1-s2.0-S0166218X16302670-main.pdf?_tid=b5db0aee-e1e1-11e7-b51a-00000aab0f02&acdnat=1513374708_82e3d74b75420ea8adca800b18dc4e43"
}