Alexandroff pretopologies for structuring the digital plane

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F17%3APU119234" target="_blank" >RIV/00216305:26210/17:PU119234 - isvavai.cz</a>

Výsledek na webu

<a href="https://ac.els-cdn.com/S0166218X16302670/1-s2.0-S0166218X16302670-main.pdf?_tid=b5db0aee-e1e1-11e7-b51a-00000aab0f02&acdnat=1513374708_82e3d74b75420ea8adca800b18dc4e43" target="_blank" >https://ac.els-cdn.com/S0166218X16302670/1-s2.0-S0166218X16302670-main.pdf?_tid=b5db0aee-e1e1-11e7-b51a-00000aab0f02&acdnat=1513374708_82e3d74b75420ea8adca800b18dc4e43</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.dam.2016.06.002" target="_blank" >10.1016/j.dam.2016.06.002</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Alexandroff pretopologies for structuring the digital plane

Popis výsledku v původním jazyce

We explore the possibility of employing Alexandroff pretopologies as structures on the digital plane Z^2 convenient for the study of geometric and topological properties of digital images. These pretopologies are known to be in one-to-one correspondence with reflexive binary relations so that graph-theoretic methods may be used when investigating them. We discuss such Alexandroff pretopologies on Z2 that possess a rich variety of digital Jordan curves obtained as circuits in a natural graph with the vertex set Z2. Of these pretopologies, we focus on the minimal ones and study their quotient pretopologies on Z2 which are shown to allow for various digital Jordan curve theorems. We also develop a method for identifying Jordan curves in the minimal pretopological spaces by using Jordan curves in one of their quotient spaces. Using this method, we conclude the paper with proving a digital Jordan curve theorem for the minimal pretopologies.

Název v anglickém jazyce

Alexandroff pretopologies for structuring the digital plane

Popis výsledku anglicky

We explore the possibility of employing Alexandroff pretopologies as structures on the digital plane Z^2 convenient for the study of geometric and topological properties of digital images. These pretopologies are known to be in one-to-one correspondence with reflexive binary relations so that graph-theoretic methods may be used when investigating them. We discuss such Alexandroff pretopologies on Z2 that possess a rich variety of digital Jordan curves obtained as circuits in a natural graph with the vertex set Z2. Of these pretopologies, we focus on the minimal ones and study their quotient pretopologies on Z2 which are shown to allow for various digital Jordan curve theorems. We also develop a method for identifying Jordan curves in the minimal pretopological spaces by using Jordan curves in one of their quotient spaces. Using this method, we conclude the paper with proving a digital Jordan curve theorem for the minimal pretopologies.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/LO1202" target="_blank" >LO1202: NETME CENTRE PLUS</a><br>

Návaznosti

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

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Discrete Applied Mathematics

ISSN

0166-218X

e-ISSN

1872-6771

Svazek periodika

216

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

12

Strana od-do

323-334

Kód UT WoS článku

000390504100002

EID výsledku v databázi Scopus

2-s2.0-84977618285