title: The number of N-point digital discs.
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 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.
authors.affiliation: School of Mathematics, Cardiff University, Cardiff, UK. Huxley@cf.ac.uk
authors.forename: Martin N
authors.initials: MN
authors.lastname: Huxley
authors.forename: Jovisa
authors.initials: J
authors.lastname: Zunić
mesh_terms: 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