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On the Number of Digital Discs

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Abstract

A digital disc is defined as the set of all integer points inside of a given real disc. In this paper we show that there are no more than

$$n^2 + {\mathcal{O}}\left( {n^{\frac{{265}}{{146}}} \cdot \left( {\log n} \right)^{\frac{{315}}{{146}}} } \right)$$

different (up to translations) digital discs consisting of n points.

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  1. Department of Computer Science, Exeter University, North Park Road, Harrison Building, Exeter, EX4 4QF, UK

    Joviša Žunić

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  1. Joviša Žunić
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Žunić, J. On the Number of Digital Discs. Journal of Mathematical Imaging and Vision 21, 199–204 (2004). https://doi.org/10.1023/B:JMIV.0000043736.15525.ed

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