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On Some Local Topological Properties of Naive Discrete Sphere

  • Nabhasmita Sen
  • Ranita Biswas
  • Partha Bhowmick
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9667)

Abstract

Discretization of sphere in the integer space follows a particular discretization scheme, which, in principle, conforms to some topological model. This eventually gives rise to interesting topological properties of a discrete spherical surface, which need to be investigated for its analytical characterization. This paper presents some novel results on the local topological properties of the naive model of discrete sphere. They follow from the bijection of each quadraginta octant of naive sphere with its projection map called f -map on the corresponding functional plane and from the characterization of certain jumps in the f-map. As an application, we have shown how these properties can be used in designing an efficient reconstruction algorithm for a naive spherical surface from an input voxel set when it is sparse or noisy.

Keywords

Discrete sphere Functional plane 3D imaging Digital topology Digital geometry 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Nabhasmita Sen
    • 1
  • Ranita Biswas
    • 1
  • Partha Bhowmick
    • 1
  1. 1.Department of Computer Science and EngineeringIndian Institute of TechnologyKharagpurIndia

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