On the number of digitisations of a disc depending on its position

Huxley, Martin Neil and Zunic, Jovisa 2004. On the number of digitisations of a disc depending on its position. Combinatorial Image Analysis, Lecture Notes in Computer Science, vol. 3322. Springer, pp. 219-231. (10.1007/978-3-540-30503-3_17)

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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))ÇZ2D(R(ab))=D(R(ab))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.

Item Type:	Book Section
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Springer
Last Modified:	04 Jun 2017 04:01
URI:	https://orca.cardiff.ac.uk/id/eprint/31002

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