Relation-induced connectedness in the digital plane View Full Text


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Article Info

DATE

2018-02

AUTHORS

Josef Šlapal

ABSTRACT

We introduce and discuss a connectedness induced by n-ary relations (n>1 an integer) on their underlying sets. In particular, we focus on certain n-ary relations with the induced connectedness allowing for a definition of digital Jordan curves. For every integer n>1, we introduce one such n-ary relation on the digital plane Z2 and prove a digital analogue of the Jordan curve theorem for the induced connectedness. It follows that these n-ary relations may be used as convenient structures on the digital plane for the study of geometric properties of digital images. For n=2, such a structure coincides with the (specialization order of the) Khalimsky topology and, for n>2, it allows for a variety of Jordan curves richer than that provided by the Khalimsky topology. More... »

PAGES

75-90

References to SciGraph publications

  • 1991-06. A Jordan surface theorem for three-dimensional digital spaces in DISCRETE & COMPUTATIONAL GEOMETRY
  • 2000. Digital Jordan Curve Theorems in DISCRETE GEOMETRY FOR COMPUTER IMAGERY
  • 2007-06. Digital Surfaces and Boundaries in Khalimsky Spaces in JOURNAL OF MATHEMATICAL IMAGING AND VISION
  • 2009. Jordan Curve Theorems with Respect to Certain Pretopologies on $\mathbb Z^2$ in DISCRETE GEOMETRY FOR COMPUTER IMAGERY
  • 2008. Graph Theory in NONE
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/s00010-017-0508-5

    DOI

    http://dx.doi.org/10.1007/s00010-017-0508-5

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1091762505


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