Publication Details

A convenient graph connectedness for digital imagery

ŠLAPAL, J. A convenient graph connectedness for digital imagery. In High Performance Computing in Science and Engineering 2019. Lecture Notes in Computer Science. Lecture Notes in Computer Science. Cham: Springer International Publishing, 2021. p. 150-162. ISBN: 978-3-030-67076-4. ISSN: 0302-9743.
Czech title
Vhodný grafová souvislost pro digitální zobrazování
Type
conference paper
Language
English
Authors
Šlapal Josef, prof. RNDr., CSc. (IM DAAG)
URL
Keywords

Simple undirected graph, connectedness, digital plane, Khalimsky topology, Jordan curve theorem.

Abstract

In a simple undirected graph, we introduce a special connectedness induced by a set of paths of length 2. We focus on the 8-adjacency graph (with the vertex set Z^2) and study the connectedness induced by a certain set of paths of length 2 in the graph. For this connectedness, we prove a digital Jordan curve theorem by determining the Jordan curves, i.e., the circles in the graph that separate  Z^2 into exactly two connected components.

Published
2021
Pages
150–162
Journal
Lecture Notes in Computer Science, vol. 2021, no. 12456, ISSN 0302-9743
Proceedings
High Performance Computing in Science and Engineering 2019
Series
Lecture Notes in Computer Science
ISBN
978-3-030-67076-4
Publisher
Springer International Publishing
Place
Cham
DOI
10.1007/978-3-030-67077-1_9
EID Scopus
2-s2.0-85101308238
BibTeX 
@inproceedings{BUT168483,
  author="Josef {Šlapal}",
  title="A convenient graph connectedness for digital imagery",
  booktitle="High Performance Computing in Science and Engineering 2019",
  year="2021",
  series="Lecture Notes in Computer Science",
  journal="Lecture Notes in Computer Science",
  volume="2021",
  number="12456",
  pages="150--162",
  publisher="Springer International Publishing",
  address="Cham",
  doi="10.1007/978-3-030-67077-1\{_}9",
  isbn="978-3-030-67076-4",
  issn="0302-9743",
  url="https://www.springer.com/gp/book/9783030670764"
}
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