On the Number of Digital Straight Line Segments
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Accuracy of Zernike Moments for Image Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficiency of Characterizing Ellipses and Ellipsoids by Discrete Moments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multigrid Convergence of Calculated Features in Image Analysis
Journal of Mathematical Imaging and Vision
Digitized Circular Arcs: Characterization and Parameter Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Number of Digital Discs
Journal of Mathematical Imaging and Vision
Different Digitisations of Displaced Discs
Foundations of Computational Mathematics
On the recovery of a function on a circular domain
IEEE Transactions on Information Theory
Computing upper and lower bounds of rotation angles from digital images
Pattern Recognition
The number of khalimsky-continuous functions between two points
IWCIA'11 Proceedings of the 14th international conference on Combinatorial image analysis
| Hi-index | 0.14 |
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 {\cal D}_{N} = {\cal O}(N^{2}) was shown recently; no corresponding lower bound is known. In this paper, we refine the upper bound to {\cal D}_{N} = {\cal O}(N), which seems to be the true order of magnitude, and we show that the average \overline{\cal D}_{N} = \left({\cal D}_{1} + {\cal D}_{2} + \ldots + {\cal D}_{N}\right)/N has upper and lower bounds which are of polynomial growth in N.