A relational generalization of the Khalimsky topology
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26210%2F17%3APU126006" target="_blank" >RIV/00216305:26210/17:PU126006 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-319-59108-7_11" target="_blank" >http://dx.doi.org/10.1007/978-3-319-59108-7_11</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-59108-7_11" target="_blank" >10.1007/978-3-319-59108-7_11</a>
Alternative languages
Result language
angličtina
Original language name
A relational generalization of the Khalimsky topology
Original language description
We discuss certain n-ary relations (n > 1 an integer) and show that each of them induces a connectedness on its underlying set. Of these n-ary relations, we study a particular one on the digital plane Z2 for every integer n > 1. As the main result, for each of the n-ary relations studied, we 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.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Combinatorial Image Analysis
ISBN
978-3-319-59107-0
ISSN
0302-9743
e-ISSN
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Number of pages
10
Pages from-to
132-141
Publisher name
Springer
Place of publication
Switzerland
Event location
Plovdiv
Event date
Jun 19, 2017
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000432061200011