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arXiv · 1602.03734

Strongly Near Voronoi Nucleus Clusters

J. F. Peters·E. Inan
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Abstract

This paper introduces nucleus clustering in Voronoi tessellations of plane surfaces with applications in the geometry of digital images. A \emph{nucleus cluster} is a collection of Voronoi regions that are adjacent to a Voronoi region called the cluster nucleus. Nucleus clustering is a carried out in a strong proximity space. Of particular interest is the presence of maximal nucleus clusters in a tessellation. Among all of the possible nucleus clusters in a Voronoi tessellation, clusters with the highest number of adjacent polygons are called \emph{maximal nucleus clusters}. The main results in this paper are that strongly near nucleus clusters are strongly descriptively near and every collection of Voronoi regions in a tessellation of a plane surface is a Zelins'kyi-Soltan-Kay-Womble convexity structure.

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J. F. Peters, E. Inan. 2016-01-29. Strongly Near Voronoi Nucleus Clusters. https://arxiv.org/abs/1602.03734

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