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dc.contributor.authorHuxley, Martinen
dc.contributor.authorŽunić, Jovišaen
dc.date.accessioned2020-05-01T20:28:57Z-
dc.date.available2020-05-01T20:28:57Z-
dc.date.issued2016-11-01en
dc.identifier.issn0924-9907en
dc.identifier.urihttp://researchrepository.mi.sanu.ac.rs/handle/123456789/1911-
dc.description.abstractConfigurations of integer lattice points inside a closed curve are a permanent topic in different research areas: from number theory to digital image analysis. This paper deals with the digital N-discs—the sets consisting of N integer lattice points which fall inside a circle. A digital N-disc corresponds to a digital image of a real circular discs, which consists of N pixels. We show that, for a large positive integer N, the average number of digital N-discs is asymptotic to 2N when N runs through a set of intervals, whose length is upper bounded by N47 / 58. In addition, we show that 2N is the best possible asymptotic estimate (the error term is ignored), for the number of digital N-discs. Such an asymptotic estimate is reached for almost all digital N-discs, for N in an interval, of the length N47 / 58. This improves result of Huxley and Žunić (IEEE Trans Pattern Anal Mach Intell 29:159–161, 2007), where an O(N) upper bound, for the number of digital N-discs, has been proven.en
dc.publisherSpringer Link-
dc.relation.ispartofJournal of Mathematical Imaging and Visionen
dc.subjectDigital disc | Digital geometry | Image processingen
dc.titleThe Number of Different Digital N-Discsen
dc.typeArticleen
dc.identifier.doi10.1007/s10851-016-0643-yen
dc.identifier.scopus2-s2.0-84960101008en
dc.relation.firstpage403en
dc.relation.lastpage408en
dc.relation.issue3en
dc.relation.volume56en
dc.description.rankM21a-
item.cerifentitytypePublications-
item.openairetypeArticle-
item.grantfulltextnone-
item.openairecristypehttp://purl.org/coar/resource_type/c_18cf-
item.fulltextNo Fulltext-
crisitem.author.orcid0000-0002-1271-4153-
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