2016/01/29 by James F. Peters, J. F. Peters, Peters, J. F. +3
Mathematics · Physics and Astronomy · #68T10 #Dark Matter and Cosmic Phenomena #FOS: Mathematics #Metric Geometry (math.MG) #Noncommutative and Quantum Gravity Theories #Primary 54E05 #Quantum many-body systems #Secondary 62H30 #math.MG #msc:54E05 #msc:62H30 #msc:68T10
paper · pdf · doi:10.48550/arxiv.1602.03734
7 pages, 2 figures
openalex publication_date 2016/01/29 · arxiv created 2016/02/12 · arxiv updated 2016/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper introduces nucleus clustering in Voronoi tessellations of plane surfaces with applications in the geometry of digital images. A 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 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.