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The Number of N-Point Digital Discs

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2 Author(s)
Huxley, M.N. ; Sch. of Math., Cardiff Univ. ; Zunic, J.

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

Published in:

Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:29 ,  Issue: 1 )

Date of Publication:

Jan. 2007

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