Abstract
The digitization D(R,(a,b)) of a real disc D(R, (a ,b)) having radius R and the centre (a, b) consists of all integer points inside of D(R, (a,b)), i.e., \(D(R,(a,b))=D(R,(a,b))\cap \mathcal{Z}^{2}\). In this paper we show that that there are
3πR 21O(R 339/208 ·(log R)18627/8320)
different (up to translations) digitizations of discs having the radius R. More formally,
#D(R, (a, b)) | a and b vary through [0, 1)
3πR 21O(R 339/208 ·(log R)18627/8320)
The result is of an interest in the area of digital image processing because it describes (in, let say, a combinatorial way) how big the impact of the object position on its digitization can be.
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Huxley, M.N., Žunić, J. (2004). On the Number of Digitizations of a Disc Depending on Its Position. In: Klette, R., Žunić, J. (eds) Combinatorial Image Analysis. IWCIA 2004. Lecture Notes in Computer Science, vol 3322. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30503-3_17
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DOI: https://doi.org/10.1007/978-3-540-30503-3_17
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