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Structuring Digital Spaces by Path-Partition Induced Closure Operators on Graphs

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Computational Modeling of Objects Presented in Images. Fundamentals, Methods, and Applications (CompIMAGE 2016)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10149))

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Abstract

We study closure operators on graphs which are induced by path partitions, i.e., certain sets of paths of the same lengths in these graphs. We investigate connectedness with respect to the closure operators studied. In particular, the closure operators are discussed that are induced by path partitions of some natural graphs on the digital spaces \({\mathbb {Z}}^n\), \(n>0\) a natural number. For the case \(n=2\), i.e., for the digital plane \({\mathbb {Z}}^2\), the induced closure operators are shown to satisfy an analogue of the Jordan curve theorem, which allows using them as convenient background structures for studying digital images.

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Acknowledgement

This work was supported by Ministry of Education, Youth and Sports of the Czech Republic from the National Programme of Sustainability (NPU II) project “IT4Innovations Excellence in Science - LQ1602”.

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Correspondence to Josef Šlapal .

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Šlapal, J. (2017). Structuring Digital Spaces by Path-Partition Induced Closure Operators on Graphs. In: Barneva, R., Brimkov, V., Tavares, J. (eds) Computational Modeling of Objects Presented in Images. Fundamentals, Methods, and Applications. CompIMAGE 2016. Lecture Notes in Computer Science(), vol 10149. Springer, Cham. https://doi.org/10.1007/978-3-319-54609-4_3

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  • DOI: https://doi.org/10.1007/978-3-319-54609-4_3

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  • Online ISBN: 978-3-319-54609-4

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