Authors: Huxley, Martin
Žunić, Joviša 
Title: On the number of digitizations of a disc depending on its position
Journal: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume: 3322
First page: 219
Last page: 231
Conference: International Workshop on Combinatorial Image Analysis, IWCIA 2004
Issue Date: 1-Dec-2004
Rank: M23
ISBN: 978-3-540-23942-0
ISSN: 0302-9743
DOI: 10.1007/978-3-540-30503-3_17
The digitization D(Ra, b)) of a real disc D(Ra, b)) having radius R and the centre (a, b) consists of all integer points inside of D(Ra, b)), i.e., D(Ra, b)) = D(Ra, b)) ∩ Z 2. In this paper we show that that there are 3πR 2 + O (R 339/208 . (logR) 18627/8320) different (up to translations) digitizations of discs having the radius R. More formally, #{D(Ra, b)) | a and b vary through [0,1)} = 3πR 2 + O (R 339/208 . (logR) 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.
Keywords: Digital disc | Enumeration | Lattice points
Publisher: Springer Link

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