Detail publikace

Alexandroff pretopologies for structuring the digital plane

ŠLAPAL, J.

Originální název

Alexandroff pretopologies for structuring the digital plane

Typ

článek v časopise ve Web of Science, Jimp

Jazyk

angličtina

Originální abstrakt

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.

Klíčová slova

Digital plane, Jordan curve, Alexandroff pretopology, quotient pretopology

Autoři

ŠLAPAL, J.

Vydáno

15. 1. 2017

Nakladatel

Elsevier

Místo

Nizozemsko

ISSN

0166-218X

Periodikum

Discrete Applied Mathematics

Ročník

216

Číslo

2

Stát

Nizozemsko

Strany od

323

Strany do

334

Strany počet

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"
}