A ternary relation for structuring the digital plane

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dc.contributor.authorŠlapal, Josefcs
dc.coverage.issue01012cs
dc.coverage.volume9cs
dc.date.issued2017-02-28cs
dc.description.abstractWe 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.&nbsp;We introduce a particular plain ternary relation on the digital plane Z^2 and, as the main result, we prove a digital&nbsp;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.<p>&nbsp;en
dc.description.abstractWe 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.&nbsp;We introduce a particular plain ternary relation on the digital plane Z^2 and, as the main result, we prove a digital&nbsp;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.<p>&nbsp;en
dc.formattextcs
dc.format.extent1-5cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationITM Web of Conferences. 2017, vol. 9, issue 01012, p. 1-5.en
dc.identifier.doi10.1051/itmconf/20170901012cs
dc.identifier.issn2271-2097cs
dc.identifier.orcid0000-0001-8843-6842cs
dc.identifier.other144501cs
dc.identifier.researcheridK-2755-2015cs
dc.identifier.scopus6602234420cs
dc.identifier.urihttp://hdl.handle.net/11012/195570
dc.language.isoencs
dc.publisherEDP Sciencescs
dc.relation.ispartofITM Web of Conferencescs
dc.relation.urihttps://www.fit.vut.cz/research/publication/11594/cs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/2271-2097/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectTernary relationen
dc.subjectconnectednessen
dc.subjectdigital planeen
dc.subjectJordan curve theoremen
dc.subjectTernary relation
dc.subjectconnectedness
dc.subjectdigital plane
dc.subjectJordan curve theorem
dc.titleA ternary relation for structuring the digital planeen
dc.title.alternativeA ternary relation for structuring the digital planeen
dc.type.driverconferenceObjecten
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-144501en
sync.item.dbtypeVAVen
sync.item.insts2025.10.14 14:13:13en
sync.item.modts2025.10.14 10:41:42en
thesis.grantorVysoké učení technické v Brně. Fakulta informačních technologií. Fakulta informačních technologiícs
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