Detail publikačního výsledku

A relational generalization of the Khalimsky topology

ŠLAPAL, J.

Originální název

A relational generalization of the Khalimsky topology

Anglický název

A relational generalization of the Khalimsky topology

Druh

Stať ve sborníku v databázi WoS či Scopus

Originální abstrakt

We discuss certain n-ary relations (n > 1 an integer) and show that each of them induces a connectedness on its underlying set. Of these n-ary relations, we study a particular one on the digital plane Z2 for every integer n > 1. As the main result, for each of the n-ary relations studied, we prove a digital analogue of the Jordan curve theorem for the induced connectedness. It follows that these n-ary relations may be used as convenient structures on the digital plane for the study of geometric properties of digital images. For n = 2, such a structure coincides with the (specialization order of the) Khalimsky topology and, for n > 2, it allows for a variety of Jordan curves richer than that provided by the Khalimsky topology.

Anglický abstrakt

We discuss certain n-ary relations (n > 1 an integer) and show that each of them induces a connectedness on its underlying set. Of these n-ary relations, we study a particular one on the digital plane Z2 for every integer n > 1. As the main result, for each of the n-ary relations studied, we prove a digital analogue of the Jordan curve theorem for the induced connectedness. It follows that these n-ary relations may be used as convenient structures on the digital plane for the study of geometric properties of digital images. For n = 2, such a structure coincides with the (specialization order of the) Khalimsky topology and, for n > 2, it allows for a variety of Jordan curves richer than that provided by the Khalimsky topology.

Klíčová slova

n-ary relation, digital plane, Khalimsky topology, Jordan curve theorem

Klíčová slova v angličtině

n-ary relation, digital plane, Khalimsky topology, Jordan curve theorem

Autoři

ŠLAPAL, J.

Rok RIV

2018

Vydáno

01.06.2017

Nakladatel

Springer

Místo

Switzerland

ISBN

978-3-319-59107-0

Kniha

Combinatorial Image Analysis

Edice

Lecture Notes in Computer Sciences

ISSN

0302-9743

Periodikum

Lecture Notes in Computer Science

Svazek

10256

Stát

Spolková republika Německo

Strany od

132

Strany do

141

Strany počet

10

BibTex

@inproceedings{BUT142992,
  author="Josef {Šlapal}",
  title="A relational generalization of the Khalimsky topology",
  booktitle="Combinatorial Image Analysis",
  year="2017",
  series="Lecture Notes in Computer Sciences",
  journal="Lecture Notes in Computer Science",
  volume="10256",
  number="10256",
  pages="132--141",
  publisher="Springer",
  address="Switzerland",
  doi="10.1007/978-3-319-59108-7\{_}11",
  isbn="978-3-319-59107-0",
  issn="0302-9743"
}