Ternární relace pro strukturování digitální roviny

 dc.contributor.author Šlapal, Josef cs dc.date.accessioned 2020-10-29T10:20:29Z dc.date.available 2020-10-29T10:20:29Z dc.date.issued 2017-02-28 cs dc.identifier.citation ITM Web of Conferences. 2017, vol. 9, issue 01012, p. 1-5. en dc.identifier.issn 2271-2097 cs dc.identifier.other 144501 cs dc.identifier.uri http://hdl.handle.net/11012/195570 dc.description.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. en dc.description.abstract 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. cs dc.format text cs dc.format.extent 1-5 cs dc.format.mimetype application/pdf cs dc.language.iso en cs dc.publisher EDP Sciences cs dc.relation.ispartof ITM Web of Conferences cs dc.relation.uri https://www.fit.vut.cz/research/publication/11594/ cs dc.rights Creative Commons Attribution 4.0 International cs dc.rights.uri http://creativecommons.org/licenses/by/4.0/ cs dc.subject Ternary relation en dc.subject connectedness en dc.subject digital plane en dc.subject Jordan curve theorem en dc.title A ternary relation for structuring the digital plane en dc.title.alternative Ternární relace pro strukturování digitální roviny cs thesis.grantor Vysoké učení technické v Brně. Fakulta informačních technologií. Fakulta informačních technologií cs sync.item.dbid VAV-144501 en sync.item.dbtype VAV en sync.item.insts 2022.10.03 12:53:32 en sync.item.modts 2022.10.03 12:14:54 en dc.coverage.issue 01012 cs dc.coverage.volume 9 cs dc.identifier.doi 10.1051/itmconf/20170901012 cs dc.rights.access openAccess cs dc.rights.sherpa http://www.sherpa.ac.uk/romeo/issn/2271-2097/ cs dc.type.driver conferenceObject en dc.type.status Peer-reviewed en dc.type.version publishedVersion en
﻿

### This item appears in the following Collection(s)

Except where otherwise noted, this item's license is described as Creative Commons Attribution 4.0 International