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Different digitizations of displaced discs

Huxley, Martin Neil and Zunic, Jovisa 2006. Different digitizations of displaced discs. Foundations of computational mathematics 6 (2) , pp. 255-268. 10.1007/s10208-005-0177-y

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Abstract

The digitisation {D}(R,(a,b)) of a real disc D(R,(a,b)) having radius R and centre (a,b) consists of all integer points inside D(R,(a,b)), i.e. D(R,(a,b))=D(R,(a,b)){Z}^2. In this paper we show that there are 4\pi R^2+O(R^{339/208}\log R)^{18627/8320})different (up to translations) digitisations of discs having radius R. More formally, {D}(R,(a,b))\mid a{ and }b { vary through }[0,1)\}=4\pi R^2+O(R^{339/208}(\log R)^{18627/8320}). The result is of interest in the area of digital image processing because it describes how large the impact of the object position can be on its digitisation.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Computer Science & Informatics
Mathematics
Publisher: Springer Verlag
ISSN: 1615-3383
Last Modified: 04 Jun 2017 01:41
URI: http://orca-mwe.cf.ac.uk/id/eprint/1766

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