2017/03/22 by James F. Peters, Peters, J. F.
Computer Science · #54E05 #68U05 #Computational Geometry (cs.CG) #Digital Image Processing Techniques #FOS: Computer and information sciences #Rough Sets and Fuzzy Logic #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.1704.05909
openalex publication_date 2017/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article introduces a theory of proximal nerve complexes and nerve spokes, restricted to the triangulation of finite regions in the Euclidean plane. A nerve complex is a collection of filled triangles with a common vertex, covering a finite region of the plane. Structures called k-spokes, k≥ 1, are a natural extension of nerve complexes. A k-spoke is the union of a collection of filled triangles that pairwise either have a common edge or a common vertex. A consideration of the closeness of nerve complexes leads to a proximal view of simplicial complexes. A practical application of proximal nerve complexes is given, briefly, in terms of object shape geometry in digital images.