Strongly Near Voronoi Nucleus Clusters

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.