Publication detail

Alexandroff pretopologies for structuring the digital plane

ŠLAPAL, J.

English title

Alexandroff pretopologies for structuring the digital plane

Type

WoS Article

Language

en

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 in English

Digital plane, Jordan curve, Alexandroff pretopology, quotient pretopology

Released

2017-01-15

Publisher

Elsevier

Location

Nizozemsko

ISSN

0166-218X

Volume

216

Number

2

Pages from–to

323–334

Pages count

12

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"
}