On Correcting the Uneveness of Angle Distributions Arising from Integer Ratios Lying in Restricted Portions of the Farey Plane

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dc.contributor.authorSvalbe, Imants D
dc.contributor.authorKingston, Andrew
dc.date.accessioned2015-12-10T22:43:24Z
dc.date.issued2004
dc.date.updated2015-12-09T11:14:19Z
dc.description.abstractIn 2D discrete projcctive transforms, projection angles correspond to lines linking pixels at integer multiples of the x and y image grid spacing. To make the projection angle set non-redundant, the integer ratios are chosen from the set of relatively prime fractions given by the Farcy sequence. To sample objects uniformly, the set of projection angles should be uniformly distributed. The unevenness function measures the deviation of an angle distribution from a uniformly increasing sequence of angles. The allowed integer multiples are restricted by the size of the discrete image array or by functional limits imposed on the range of x and y increments for a particular transform. This paper outlines a method to compensate the unevenness function for the geometric effects of different restrictions on the ranges of integers selected to form these ratios. This geometric correction enables a direct comparison to be made of the effective uniformity of an angle set formed over selected portions of the Farey Plane. This result has direct application in comparing the smoothness of digital angle sets.
dc.identifier.issn0302-9743
dc.identifier.urihttp://hdl.handle.net/1885/58150
dc.publisherSpringer
dc.sourceLecture Notes in Computer Science (LNCS)
dc.subjectKeywords: Discrete image processing; Discrete Radon transforms; Farey sequences and digital angles
dc.titleOn Correcting the Uneveness of Angle Distributions Arising from Integer Ratios Lying in Restricted Portions of the Farey Plane
dc.typeJournal article
local.bibliographicCitation.lastpage121
local.bibliographicCitation.startpage110
local.contributor.affiliationSvalbe, Imants D, Monash University
local.contributor.affiliationKingston, Andrew, College of Physical and Mathematical Sciences, ANU
local.contributor.authoremailu4438507@anu.edu.au
local.contributor.authoruidKingston, Andrew, u4438507
local.description.embargo2037-12-31
local.description.notesImported from ARIES
local.identifier.absfor020405 - Soft Condensed Matter
local.identifier.ariespublicationu9210271xPUB429
local.identifier.citationvolumeLNCS3322
local.identifier.scopusID2-s2.0-33845238895
local.identifier.uidSubmittedByu9210271
local.type.statusPublished Version

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