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 t...
| Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence. - 1979. - 29(2007), 1 vom: 16. Jan., Seite 159-61 |
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| Format: | Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2007
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on pattern analysis and machine intelligence |
| Schlagworte: | Journal Article Research Support, Non-U.S. Gov't |
| Zusammenfassung: | 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 |
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| Beschreibung: | Date Completed 30.01.2007 Date Revised 19.11.2006 published: Print Citation Status MEDLINE |
| ISSN: | 1939-3539 |