DC Field | Value | Language |
---|---|---|
dc.contributor.author | Huxley, Martin | en |
dc.contributor.author | Žunić, Joviša | en |
dc.date.accessioned | 2020-05-01T20:28:57Z | - |
dc.date.available | 2020-05-01T20:28:57Z | - |
dc.date.issued | 2016-11-01 | en |
dc.identifier.issn | 0924-9907 | en |
dc.identifier.uri | http://researchrepository.mi.sanu.ac.rs/handle/123456789/1911 | - |
dc.description.abstract | Configurations 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.publisher | Springer Link | - |
dc.relation.ispartof | Journal of Mathematical Imaging and Vision | en |
dc.subject | Digital disc | Digital geometry | Image processing | en |
dc.title | The Number of Different Digital N-Discs | en |
dc.type | Article | en |
dc.identifier.doi | 10.1007/s10851-016-0643-y | en |
dc.identifier.scopus | 2-s2.0-84960101008 | en |
dc.relation.firstpage | 403 | en |
dc.relation.lastpage | 408 | en |
dc.relation.issue | 3 | en |
dc.relation.volume | 56 | en |
dc.description.rank | M21a | - |
item.fulltext | No Fulltext | - |
item.openairetype | Article | - |
item.grantfulltext | none | - |
item.cerifentitytype | Publications | - |
item.openairecristype | http://purl.org/coar/resource_type/c_18cf | - |
crisitem.author.orcid | 0000-0002-1271-4153 | - |
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