STRONGLY PROXIMAL EDELSBRUNNER-HARER NERVES
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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)
- E. A-iyeh, "Measure of tessellation quality of Vorono¨ı meshes", Theory and Application of Math. and Comp. Sci, 5(2), pp.158~185 (2015)
- A. Al-Shammari, "Re-evaluating the use of Vorono¨ı tessellations in the assessment of oxygen supply from capillaries in muscle", Bull. Math. Biol, 74(9), pp.2204~2231 (2016)
- A. Di Concilio, "Topologizing homeomorphism groups of rimcompact spaces", Topology and its Applications, 153(11), pp.1867~1885 (2006)
- A. Di Concilio, "Point-free geometries: Proximities and quasi-metrics", Math. in Comp. Sci, 7(1), pp.31~42 (2013)
- Q. Du, "Advances in studies and applications of centroidal Vorono¨ı tessellations", Numer. Math. Theory Methods Appl, 3(2), pp.119~142 (2010)
- G. Duyckaerts, "Vorono¨ı tessellation to study the numerical density and the spatial distribution of neurons", J. of Chemical Neuroanatomy, 20(1), pp.83~92 (2000)
- H. Edelsbrunner, "Geometry and topology of mesh generation", pp.209~ (2001), Cambridge University Press
- H. Edelsbrunner, "A short course in computational geometry and topology", pp.110~ (2014), Springer
- H. Edelsbrunner, "Computational topology. an introduction", pp.xii~110 (2010), American Mathematical Society
- H. Edelsbrunner, "Computational topology. an introduction", pp.xii~241 (2010), Amer. Math. Soc.
- S. Fukushige, "Polygon visibility ordering via Vorono¨ı diagrams", Visual Comput, 23(7), pp.503~511 (2007)
- C. Gold, "Research Trends in Geographic Information Science", pp.79~94 (2009), Springer
- C. Guadagni, "Bornological convergences on local proximity spaces and ωμ-metric spaces", Ph.D., pp.2015
- E. ˙Inan, "Algebraic structures on nearness approximation spaces", Ph.D., Department of Mathematics, pp.2015
- D.C. Kay, "Automatic convexity theory and relationships between the carath`eodory, helly and radon numbers", Pacific Journal of Math, 38(2), pp.471~485 (1971)
- M.W. Lodato, "On topologically induced generalized proximity relations", ph.d, pp.1962
- M.W. Lodato, "On topologically induced generalized proximity relations i", Proc. Amer. Math. Soc, 15, pp.417~422 (1964)
- M.W. Lodato, "On topologically induced generalized proximity relations ii", Pacific J. Math, 17, pp.131~135 (1966)
- S.A. Naimpally, "Proximity spaces", pp.10~128 (1970), Cambridge University Press
- S.A. Naimpally, "Proximity approach to problems in topology and analysis", pp.73~ (2009), Oldenbourg Verlag
- S.A. Naimpally, "Topology with applications. Topological spaces via near and far", pp.xv~277 (2013), World Scientific
- J. F. Peters, "Proximal Delaunay triangulation regions", Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집), 18(4), pp.501~510 (2015), 장전수학회
- J.F. Peters, "Computational proximity. Excursions in the topology of digital images", pp.xxvi~433 (2016)
- J.F. Peters, "Proximal relator spaces", Filomat, 30(2), pp.469~472 (2016), National Library of Serbia[DOI]
- J.F. Peters, "Strong proximities on smooth manifolds and Vorono¨ı diagrams", Advances in Math.: Sci. J, 4(2), pp.91~107 (2015)
- J.F. Peters, "Strongly near proximity and hyperspace topology", arXiv, 1502(05913), pp.1~6 (2015)
- Jim Peters, "Applications of Near Sets", Notices of the American Mathematical Society, 59(04), pp.1~ (2012), American Mathematical Society (AMS)[DOI]
- James F. Peters, "Brain tissue tessellation shows absence of canonical microcircuits", Neuroscience Letters, 626, pp.99~105 (2016), Elsevier BV[DOI]
- V.P. Solan, "Introduction to the axiomatic theory of convexity [Russian with English and French summaries", pp.224~ (1984), Shtiintsa
- ´A Sz´az, "Basic tools and mild continuities in relator spaces", Acta Math. Hungar, 50(3-4), pp.177~201 (1987)
- Arturo Tozzi, "A topological approach unveils system invariances and broken symmetries in the brain", Journal of Neuroscience Research, 94(5), pp.351~365 (2016), Wiley-Blackwell[DOI]
- A. Villagran, "Non-parametric sampling approximation via Vorono¨ıtessellation, Comm", Statist. Simulation Comput, 45(2), pp.717~736 (2016)
- J. Wang, "Edge-weighted centroidal Vorono¨ı tessellation based algorithms for image segmentation", Ph.D, Department of Scientific Computing, pp.2011
- Y.B. Zelins’kyi, "Generalized convex envelopes of sets and the problem of shadow", Journal of Mathematical Sciences, 211(5), pp.710~717 (2015)
