Skip navigation
Skip navigation

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

Svalbe, Imants D; Kingston, Andrew

Description

In 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...[Show more]

dc.contributor.authorSvalbe, Imants D
dc.contributor.authorKingston, Andrew
dc.date.accessioned2015-12-10T22:43:24Z
dc.identifier.issn0302-9743
dc.identifier.urihttp://hdl.handle.net/1885/58150
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.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.description.notesImported from ARIES
local.identifier.citationvolumeLNCS3322
dc.date.issued2004
local.identifier.absfor020405 - Soft Condensed Matter
local.identifier.ariespublicationu9210271xPUB429
local.type.statusPublished Version
local.contributor.affiliationSvalbe, Imants D, Monash University
local.contributor.affiliationKingston, Andrew, College of Physical and Mathematical Sciences, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.startpage110
local.bibliographicCitation.lastpage121
dc.date.updated2015-12-09T11:14:19Z
local.identifier.scopusID2-s2.0-33845238895
CollectionsANU Research Publications

Download

File Description SizeFormat Image
01_Svalbe_On_Correcting_the_Uneveness_of_2004.pdf312.84 kBAdobe PDF    Request a copy


Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.

Updated:  20 July 2017/ Responsible Officer:  University Librarian/ Page Contact:  Library Systems & Web Coordinator