|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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