---
_id: '5800'
abstract:
- lang: eng
text: This paper presents a novel study on the functional gradation of coordinate
planes in connection with the thinnest and tunnel-free (i.e., naive) discretization
of sphere in the integer space. For each of the 48-symmetric quadraginta octants
of naive sphere with integer radius and integer center, we show that the corresponding
voxel set forms a bijection with its projected pixel set on a unique coordinate
plane, which thereby serves as its functional plane. We use this fundamental property
to prove several other theoretical results for naive sphere. First, the quadraginta
octants form symmetry groups and subgroups with certain equivalent topological
properties. Second, a naive sphere is always unique and consists of fewest voxels.
Third, it is efficiently constructible from its functional-plane projection. And
finally, a special class of 4-symmetric discrete 3D circles can be constructed
on a naive sphere based on back projection from the functional plane.
author:
- first_name: Ranita
full_name: Biswas, Ranita
id: 3C2B033E-F248-11E8-B48F-1D18A9856A87
last_name: Biswas
orcid: 0000-0002-5372-7890
- first_name: Partha
full_name: Bhowmick, Partha
last_name: Bhowmick
citation:
ama: Biswas R, Bhowmick P. On the functionality and usefulness of Quadraginta octants
of naive sphere. Journal of Mathematical Imaging and Vision. 2017;59(1):69-83.
doi:10.1007/s10851-017-0718-4
apa: Biswas, R., & Bhowmick, P. (2017). On the functionality and usefulness
of Quadraginta octants of naive sphere. Journal of Mathematical Imaging and
Vision. Springer Nature. https://doi.org/10.1007/s10851-017-0718-4
chicago: Biswas, Ranita, and Partha Bhowmick. “On the Functionality and Usefulness
of Quadraginta Octants of Naive Sphere.” Journal of Mathematical Imaging and
Vision. Springer Nature, 2017. https://doi.org/10.1007/s10851-017-0718-4.
ieee: R. Biswas and P. Bhowmick, “On the functionality and usefulness of Quadraginta
octants of naive sphere,” Journal of Mathematical Imaging and Vision, vol.
59, no. 1. Springer Nature, pp. 69–83, 2017.
ista: Biswas R, Bhowmick P. 2017. On the functionality and usefulness of Quadraginta
octants of naive sphere. Journal of Mathematical Imaging and Vision. 59(1), 69–83.
mla: Biswas, Ranita, and Partha Bhowmick. “On the Functionality and Usefulness of
Quadraginta Octants of Naive Sphere.” Journal of Mathematical Imaging and Vision,
vol. 59, no. 1, Springer Nature, 2017, pp. 69–83, doi:10.1007/s10851-017-0718-4.
short: R. Biswas, P. Bhowmick, Journal of Mathematical Imaging and Vision 59 (2017)
69–83.
date_created: 2019-01-08T20:42:08Z
date_published: 2017-09-01T00:00:00Z
date_updated: 2021-01-12T08:03:34Z
day: '01'
doi: 10.1007/s10851-017-0718-4
extern: '1'
intvolume: ' 59'
issue: '1'
language:
- iso: eng
month: '09'
oa_version: None
page: 69-83
publication: Journal of Mathematical Imaging and Vision
publication_identifier:
issn:
- '09249907'
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: On the functionality and usefulness of Quadraginta octants of naive sphere
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 59
year: '2017'
...