Publication detail

A relational generalization of the Khalimsky topology

ŠLAPAL, J.

Original Title

A relational generalization of the Khalimsky topology

English Title

A relational generalization of the Khalimsky topology

Type

conference paper

Language

en

Original Abstract

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.

English abstract

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.

Keywords

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

Released

01.06.2017

Publisher

Springer

Location

Switzerland

ISBN

978-3-319-59107-0

Book

Combinatorial Image Analysis

Edition

Lecture Notes in Computer Sciences

Edition number

10256

Pages from

132

Pages to

141

Pages count

10

Documents

BibTex


@inproceedings{BUT142992,
  author="Josef {Šlapal}",
  title="A relational generalization of the Khalimsky topology",
  annote="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.",
  address="Springer",
  booktitle="Combinatorial Image Analysis",
  chapter="142992",
  doi="10.1007/978-3-319-59108-7_11",
  edition="Lecture Notes in Computer Sciences",
  howpublished="print",
  institution="Springer",
  year="2017",
  month="june",
  pages="132--141",
  publisher="Springer",
  type="conference paper"
}