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How to Transform and Filter Images Using Iterated Function Systems

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Barnsley, Michael; Harding, Brendan; Igudesman, Konstantin

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We generalize the mathematics of fractal transformations and illustrate how it leads to a new approach to the representation and processing of digital images, and consequent novel methods for filtering, watermarking, and encryption. This work substantially generalizes earlier work on fractal tops. The approach involves fractal geometry, chaotic dynamics, and an interplay between discrete and continuous representations. The underlying mathematics is established and some applications to digital...[Show more]

dc.contributor.authorBarnsley, Michael
dc.contributor.authorHarding, Brendan
dc.contributor.authorIgudesman, Konstantin
dc.date.accessioned2015-12-07T22:21:48Z
dc.identifier.issn1936-4954
dc.identifier.urihttp://hdl.handle.net/1885/20206
dc.description.abstractWe generalize the mathematics of fractal transformations and illustrate how it leads to a new approach to the representation and processing of digital images, and consequent novel methods for filtering, watermarking, and encryption. This work substantially generalizes earlier work on fractal tops. The approach involves fractal geometry, chaotic dynamics, and an interplay between discrete and continuous representations. The underlying mathematics is established and some applications to digital imaging are described and exemplified.
dc.publisherSociety for Industrial and Applied Mathematics
dc.sourceSIAM Journal of Imaging Sciences
dc.subjectKeywords: Chaotic dynamics; Digital image; Digital imaging; Filter images; Fractal geometry; Fractal transformation; Fractal transformations; Iterated function system; Novel methods; Dynamical systems; Functions; Fractals Dynamical systems; Fractal transformations; Iterated function systems
dc.titleHow to Transform and Filter Images Using Iterated Function Systems
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume4
dc.date.issued2011
local.identifier.absfor080106 - Image Processing
local.identifier.absfor010204 - Dynamical Systems in Applications
local.identifier.ariespublicationu4685828xPUB11
local.type.statusPublished Version
local.contributor.affiliationBarnsley, Michael, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationHarding, Brendan, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationIgudesman, Konstantin, Kazan Federal University
local.description.embargo2037-12-31
local.bibliographicCitation.issue4
local.bibliographicCitation.startpage1001
local.bibliographicCitation.lastpage1028
local.identifier.doi10.1137/100815293
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciences
local.identifier.absseo970108 - Expanding Knowledge in the Information and Computing Sciences
local.identifier.absseo890301 - Electronic Information Storage and Retrieval Services
dc.date.updated2016-02-24T11:17:12Z
local.identifier.scopusID2-s2.0-80955159911
local.identifier.thomsonID000298370600002
CollectionsANU Research Publications

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