The number of N point digital discs

Huxley, Martin Neil and Žunić, Jovisa 2007. The number of N point digital discs. IEEE Transactions on Pattern Analysis and Machine Intelligence 29 (1) , pp. 159-161.

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Abstract

A digital disc is the set of all integer points inside some given disc. Let {\cal D}_{N} be the number of different digital discs consisting of N points (different up to translation). The upper bound {\cal D}_{N} = {\cal O}(N^{2}) was shown recently; no corresponding lower bound is known. In this paper, we refine the upper bound to {\cal D}_{N} = {\cal O}(N), which seems to be the true order of magnitude, and we show that the average \overline{\cal D}_{N} = \left({\cal D}_{1} + {\cal D}_{2} + \ldots + {\cal D}_{N}\right)/N has upper and lower bounds which are of polynomial growth in N.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Institute of Electrical and Electronics Engineers
ISSN:	0162-8828
Last Modified:	04 Jun 2017 04:01
URI:	https://orca.cardiff.ac.uk/id/eprint/30995

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