A ternary relation for structuring the digital plane

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26230%2F17%3APU126478" target="_blank" >RIV/00216305:26230/17:PU126478 - isvavai.cz</a>

Result on the web

<a href="http://www.fit.vutbr.cz/research/pubs/all.php?id=11594" target="_blank" >http://www.fit.vutbr.cz/research/pubs/all.php?id=11594</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1051/itmconf/20170901012" target="_blank" >10.1051/itmconf/20170901012</a>

Result language

angličtina

Original language name

A ternary relation for structuring the digital plane

Original language description

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.  

Czech name

—

Czech description

—

Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2017

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

AMCSE 2016

ISBN

—

ISSN

2271-2097

e-ISSN

—

Number of pages

5

Pages from-to

1-5

Publisher name

EDP Sciences

Place of publication

Les Ulis Cedex A

Event location

Roma

Event date

Oct 22, 2016

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

000402753800012