On the Connectivity and Smoothness of Discrete Spherical Circles

R. Biswas, P. Bhowmick, V.E. Brimkov, in:, Combinatorial Image Analysis, Springer, Cham, 2016, pp. 86–100.

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Abstract
A discrete spherical circle is a topologically well-connected 3D circle in the integer space, which belongs to a discrete sphere as well as a discrete plane. It is one of the most important 3D geometric primitives, but has not possibly yet been studied up to its merit. This paper is a maiden exposition of some of its elementary properties, which indicates a sense of its profound theoretical prospects in the framework of digital geometry. We have shown how different types of discretization can lead to forbidden and admissible classes, when one attempts to define the discretization of a spherical circle in terms of intersection between a discrete sphere and a discrete plane. Several fundamental theoretical results have been presented, the algorithm for construction of discrete spherical circles has been discussed, and some test results have been furnished to demonstrate its practicality and usefulness.
Publishing Year
Date Published
2016-01-06
Book Title
Combinatorial image analysis
Volume
9448
Page
86-100
Conference
IWCIA: International Workshop on Combinatorial Image Analysis
Conference Location
Kolkata, India
Conference Date
2015-11-24 – 2015-11-27
IST-REx-ID

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Biswas R, Bhowmick P, Brimkov VE. On the Connectivity and Smoothness of Discrete Spherical Circles. In: Combinatorial Image Analysis. Vol 9448. Lecture Notes in Computer Science. Cham: Springer; 2016:86-100. doi:10.1007/978-3-319-26145-4_7
Biswas, R., Bhowmick, P., & Brimkov, V. E. (2016). On the Connectivity and Smoothness of Discrete Spherical Circles. In Combinatorial image analysis (Vol. 9448, pp. 86–100). Cham: Springer. https://doi.org/10.1007/978-3-319-26145-4_7
Biswas, Ranita, Partha Bhowmick, and Valentin E. Brimkov. “On the Connectivity and Smoothness of Discrete Spherical Circles.” In Combinatorial Image Analysis, 9448:86–100. Lecture Notes in Computer Science. Cham: Springer, 2016. https://doi.org/10.1007/978-3-319-26145-4_7.
R. Biswas, P. Bhowmick, and V. E. Brimkov, “On the Connectivity and Smoothness of Discrete Spherical Circles,” in Combinatorial image analysis, vol. 9448, Cham: Springer, 2016, pp. 86–100.
Biswas R, Bhowmick P, Brimkov VE. 2016. On the Connectivity and Smoothness of Discrete Spherical Circles. Combinatorial image analysis. IWCIA: International Workshop on Combinatorial Image AnalysisLecture Notes in Computer Science vol. 9448. 86–100.
Biswas, Ranita, et al. “On the Connectivity and Smoothness of Discrete Spherical Circles.” Combinatorial Image Analysis, vol. 9448, Springer, 2016, pp. 86–100, doi:10.1007/978-3-319-26145-4_7.

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