Publication detail

Convenient adjacencies for structuring the digital plane

ŠLAPAL, J.

Czech title

Vhodné přilehlosti pro strukturaci digitální roviny

English title

Convenient adjacencies for structuring the digital plane

Type

journal article in Web of Science

Language

en

Original abstract

We study graphs with the vertex set Z^2 which are subgraphs of the 8- adjacency graph and have the property that certain natural cycles in these graphs are Jordan curves, i.e., separate Z^2 into exactly two connected components. Of these graphs, we determine the minimal ones and study their quotient graphs. The results obtained are used to prove digital analogues of the Jordan curve theorem for several graphs on Z^2. Thus, these graphs are shown to provide background structures on the digital plane Z^2 convenient for studying digital images.

Czech abstract

V práci jsou studovány grafy s množinou vrcholů Z^2, které jsou podgrafy grafu 8-přilehlosti a v nichž jisté přirozené kružnice jsou Jordanovými křivkami, tj. rozdělují množinu Z^2 na právš dvě souviské komponenty. Je nalezen minimální z těchto grafů a jsou studovány jeho faktorové grafy. Získané výsledky jsou použity k nalezení digitálních analogií Jordanovy věty pro několik grafů na Z^2.

English abstract

We study graphs with the vertex set Z^2 which are subgraphs of the 8- adjacency graph and have the property that certain natural cycles in these graphs are Jordan curves, i.e., separate Z^2 into exactly two connected components. Of these graphs, we determine the minimal ones and study their quotient graphs. The results obtained are used to prove digital analogues of the Jordan curve theorem for several graphs on Z^2. Thus, these graphs are shown to provide background structures on the digital plane Z^2 convenient for studying digital images.

Keywords in Czech

Jednoduchý graf, faktorový graf, souvislá množina, digitální rovina, Jordanova křivka

Keywords in English

Simple graph, quotient graph, connected set, digital plane, Jordan curve

RIV year

2015

Released

15.09.2015

Publisher

Springer

ISSN

1012-2443

Volume

75 (2015)

Number

1

Pages from–to

69–88

Pages count

10

BIBTEX


@article{BUT104915,
  author="Josef {Šlapal},
  title="Convenient adjacencies for structuring the digital plane",
  year="2015",
  volume="75 (2015)",
  number="1",
  month="September",
  pages="69--88",
  publisher="Springer",
  issn="1012-2443"
}