Title :
The Number of N-Point Digital Discs
Author :
Huxley, Martin N. ; Zunic, Jovisa
Author_Institution :
Sch. of Math., Cardiff Univ.
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 :
computational complexity; computational geometry; N-point digital disc; digital geometry; polynomial growth; Character recognition; Gaussian processes; Geometry; Indexing; Parameter estimation; Polynomials; Root mean square; Upper bound; Digital disc; digital geometry.; digitization; enumeration; Algorithms; Computer Graphics; Image Enhancement; Image Interpretation, Computer-Assisted; Imaging, Three-Dimensional; Information Storage and Retrieval; Signal Processing, Computer-Assisted;
Journal_Title :
Pattern Analysis and Machine Intelligence, IEEE Transactions on
DOI :
10.1109/TPAMI.2007.250606
