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STRONGLY PROXIMAL EDELSBRUNNER-HARER NERVES

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초록

This paper introduces Vorono¨ı mesh nuclei and maximal nuclei clusters in Voronoı tessellations of plane surfaces with applications in the geometry of digital images. Among all of the possible nucleus clusters in a Voronoı tessellation, clusters with the highest number of adjacent polygons are called maximal nucleus clusters. The main results in this paper are (i) a Vorono¨ı maximal nucleus cluster (MNC) is a strongly proximal Edelsbrunner-Harer nerve, (ii) each MNC nerve and the union of the sets in the MNC have the same homotopy type and (iii) every collection of Vorono¨ı regions in a tessellation of a plane surface is a Zelins’kyi-Soltan-Kay- Womble convexity structure.

Abstract

This paper introduces Vorono¨ı mesh nuclei and maximal nuclei clusters in Voronoı tessellations of plane surfaces with applications in the geometry of digital images. Among all of the possible nucleus clusters in a Voronoı tessellation, clusters with the highest number of adjacent polygons are called maximal nucleus clusters. The main results in this paper are (i) a Vorono¨ı maximal nucleus cluster (MNC) is a strongly proximal Edelsbrunner-Harer nerve, (ii) each MNC nerve and the union of the sets in the MNC have the same homotopy type and (iii) every collection of Vorono¨ı regions in a tessellation of a plane surface is a Zelins’kyi-Soltan-Kay- Womble convexity structure.

참고문헌 (34)

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