A ternary relation for structuring the digital plane

Loading...
Thumbnail Image
Date
2017-02-28
Advisor
Referee
Mark
Journal Title
Journal ISSN
Volume Title
Publisher
EDP Sciences
Altmetrics
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.
V práci jsou diskutovány jisté ternární relace, které  jsou nazvány jednoduché, a je ukázáno, že každá z nich indukuje souvislost na své nosné množině. Pozornost je pak věnována jisté speciální jednoduché ternární relaci na digitální rovině Z^2. Jako hlavní výsledek je dokázána Jordanova věta pro souvislost indukovanou touto relací.
Description
Citation
ITM Web of Conferences. 2017, vol. 9, issue 01012, p. 1-5.
https://www.fit.vut.cz/research/publication/11594/
Document type
Peer-reviewed
Document version
Published version
Date of access to the full text
Language of document
en
Study field
Comittee
Date of acceptance
Defence
Result of defence
Document licence
Creative Commons Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
Citace PRO