The number of N-point digital discs

IEEE Trans Pattern Anal Mach Intell. 2007 Jan;29(1):159-61. doi: 10.1109/TPAMI.2007.20.

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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Algorithms*
  • Computer Graphics*
  • Image Enhancement / methods*
  • Image Interpretation, Computer-Assisted / methods*
  • Imaging, Three-Dimensional / methods*
  • Information Storage and Retrieval / methods
  • Signal Processing, Computer-Assisted*