# On some local topological properties of naive discrete sphere

Sen N, Biswas R, Bhowmick P. 2016.On some local topological properties of naive discrete sphere. In: Computational Topology in Image Context. LNCS, vol. 9667, 253–264.

Download

**No fulltext has been uploaded. References only!**

*Book Chapter*|

*Published*|

*English*

Author

Sen, Nabhasmita;
Biswas, Ranita

^{ISTA}^{}; Bhowmick, ParthaDepartment

Series Title

LNCS

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.

Publishing Year

Date Published

2016-06-02

Book Title

Computational Topology in Image Context

Volume

9667

Page

253-264

Conference

CTIC: Computational Topology in Image Context

Conference Location

Marseille, France

Conference Date

2016-06-15 – 2016-06-17

ISBN

ISSN

eISSN

IST-REx-ID

### Cite this

Sen N, Biswas R, Bhowmick P. On some local topological properties of naive discrete sphere. In:

*Computational Topology in Image Context*. Vol 9667. Cham: Springer Nature; 2016:253-264. doi:10.1007/978-3-319-39441-1_23Sen, N., Biswas, R., & Bhowmick, P. (2016). On some local topological properties of naive discrete sphere. In

*Computational Topology in Image Context*(Vol. 9667, pp. 253–264). Cham: Springer Nature. https://doi.org/10.1007/978-3-319-39441-1_23Sen, Nabhasmita, Ranita Biswas, and Partha Bhowmick. “On Some Local Topological Properties of Naive Discrete Sphere.” In

*Computational Topology in Image Context*, 9667:253–64. Cham: Springer Nature, 2016. https://doi.org/10.1007/978-3-319-39441-1_23.N. Sen, R. Biswas, and P. Bhowmick, “On some local topological properties of naive discrete sphere,” in

*Computational Topology in Image Context*, vol. 9667, Cham: Springer Nature, 2016, pp. 253–264.Sen, Nabhasmita, et al. “On Some Local Topological Properties of Naive Discrete Sphere.”

*Computational Topology in Image Context*, vol. 9667, Springer Nature, 2016, pp. 253–64, doi:10.1007/978-3-319-39441-1_23.