Authors: Huxley, Martin
Žunić, Joviša 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: The number of N-point digital discs
Journal: IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume: 29
Issue: 1
First page: 159
Last page: 161
Issue Date: 1-Jan-2007
Rank: M21a
ISSN: 0162-8828
DOI: 10.1109/TPAMI.2007.250606
Abstract: 
A digital disc is the set of all integer points inside some given disc. Let DN be the number of different digital discs consisting of N points (different up to translation). The upper bound D N = O(N2) was shown recently; no corresponding lower bound is known. In this paper, we refine the upper bound to DN = O(N), which seems to be the true order of magnitude, and we show that the average DN = D1 + D2 + ... + DN)/N has upper and lower bounds which are of polynomial growth in N.
Keywords: Digital disc | Digital geometry | Digitization | Enumeration
Publisher: IEEE

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