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Proceedings Paper

Hyperspheres of N-sequence distances
Author(s): P. P. Das
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Paper Abstract

Let d be a metric on the n-D digital space Zn. The hypersphere Hd(r) of radius r, r integer, and center at origin is defined as Hd(r) equals {x : x (epsilon) Zn & d(x) ≤ r}. For example, Das and Chatterji studied the structure, volume and surface of such digital hyperspheres for the m-neighbor distance dnm. On generalization to dnm the N-sequence distance d(B) was proposed with the contention that these will define hyperoctagons in n-D. However, the hyperoctagonality of d(B)'s has not been established so far except for the special cases of 2- and 3-D and for dnm's in n- D. In this paper we explore the structure of the hyperspheres of d(B)'s in n-D to show that they truly are hyperoctagons. In particular we derive a formula to compute the corners of such hyperoctagons given a B and a r.

Paper Details

Date Published: 9 April 1993
PDF: 7 pages
Proc. SPIE 1832, Vision Geometry, (9 April 1993); doi: 10.1117/12.142186
Show Author Affiliations
P. P. Das, Indian Institute of Technology/Kharagpur (India)

Published in SPIE Proceedings Vol. 1832:
Vision Geometry
Robert A. Melter; Angela Y. Wu, Editor(s)

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