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ŠLAPAL, J.
Original Title
A ternary relation for structuring the digital plane
Type
conference paper
Language
English
Original Abstract
We discuss certain ternary relations, called plain, and show that each of them induces a connectedness on its underlying set. This connectedness allows for definitions of concepts of simple closed and Jordan curves. We introduce a particular plain ternary relation on the digital plane Z^2 and, as the main result, we prove a digital analogue of the Jordan curve theorem for the connectedness induced by this relation. It follows that the ternary relation introduced may be used as a convenient structure on the digital plane for the study of the geometric properties of digital images that are related to boundaries because boundaries of objects in digital images are represented by digital Jordan curves. An advantage of this structure over the Khalimsky topology is that it allows Jordan curves to turn at the acute angle /4 at some points.
Keywords
Ternary relation, connectedness, digital plane, Jordan curve theorem
Authors
Released
28. 2. 2017
Publisher
EDP Sciences
Location
Les Ulis Cedex A
ISBN
2271-2097
Periodical
ITM Web of Conferences
Year of study
9
Number
01012
State
French Republic
Pages from
1
Pages to
5
Pages count
URL
https://www.fit.vut.cz/research/publication/11594/
Full text in the Digital Library
http://hdl.handle.net/11012/195570
BibTex
@inproceedings{BUT144501, author="Josef {Šlapal}", title="A ternary relation for structuring the digital plane", booktitle="AMCSE 2016", year="2017", journal="ITM Web of Conferences", volume="9", number="01012", pages="1--5", publisher="EDP Sciences", address="Les Ulis Cedex A", doi="10.1051/itmconf/20170901012", issn="2271-2097", url="https://www.fit.vut.cz/research/publication/11594/" }