The number of N-point digital discs.
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 D(N) = O(N(2)) was shown recently; no corresponding lower bound is known. In this paper, we refine the upper bound to D(N) = O(N), which seems to be the true order of magnitude, and we show that the average [formula: see text] has upper and lower bounds which are of polynomial growth in N.
Huxley
Martin N
MN
School of Mathematics, Cardiff University, Cardiff, UK. Huxley@cf.ac.uk
Zunić
Jovisa
J
D000465:Algorithms; D003196:Computer Graphics; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D012815:Signal Processing, Computer-Assisted