Fractal Imaging Theory and Applications beyond Compression

The Atrium, University of Guelph Institutional Repository

Fractal Imaging Theory and Applications beyond Compression

Show simple item record

dc.contributor.advisor Kunze, Herb
dc.contributor.advisor La Torre, Davide
dc.contributor.author Demers, Matthew
dc.date 2012-05-07
dc.date.accessioned 2012-05-14T18:36:51Z
dc.date.available 2012-05-14T18:36:51Z
dc.date.issued 2012-05-14
dc.identifier.uri http://hdl.handle.net/10214/3634
dc.description.abstract The use of fractal-based methods in imaging was first popularized with fractal image compression in the early 1990s. In this application, one seeks to approximate a given target image by the fixed point of a contractive operator called the fractal transform. Typically, one uses Local Iterated Function Systems with Grey-Level Maps (LIFSM), where the involved functions map a parent (domain) block in an image to a smaller child (range) block and the grey-level maps adjust the shading of the shrunken block. The fractal transform is defined by the collection of optimal parent-child pairings and parameters defining the grey-level maps. Iteration of the fractal transform on any initial image produces an approximation of the fixed point and, hence, an approximation of the target image. Since the parameters defining the LIFSM take less space to store than the target image does, image compression is achieved.This thesis extends the theoretical and practical frameworks of fractal imaging to one involving a particular type of multifunction that captures the idea that there are typically many near-optimal parent-child pairings. Using this extended machinery, we treat three application areas. After discussing established edge detection methods, we present a fractal-based approach to edge detection with results that compare favourably to the Sobel edge detector. Next, we discuss two methods of information hiding: first, we explore compositions of fractal transforms and cycles of images and apply these concepts to image-hiding; second, we propose and demonstrate an algorithm that allows us to securely embed with redundancy a binary string within an image. Finally, we discuss some theory of certain random fractal transforms with potential applications to texturing. en_US
dc.description.sponsorship The Natural Sciences and Engineering Research Council and the University of Guelph helped to provide financial support for this research. en_US
dc.language.iso en en_US
dc.rights.uri http://creativecommons.org/licenses/by/2.5/ca/ *
dc.subject Applied Analysis en_US
dc.subject Fractals en_US
dc.subject Imaging en_US
dc.subject Edge Detection en_US
dc.subject Iterated Function Systems en_US
dc.subject Texturing en_US
dc.subject Cryptography en_US
dc.subject Inverse Problems en_US
dc.title Fractal Imaging Theory and Applications beyond Compression en_US
dc.type Thesis en_US
dc.degree.programme Mathematics and Statistics en_US
dc.degree.name Doctor of Philosophy en_US
dc.degree.department Department of Mathematics and Statistics en_US


Files in this item

Files Size Format View Description
docthesis_finalcopy.pdf 5.053Mb PDF View/Open Doctoral Thesis

This item appears in the following Collection(s)

Show simple item record

http://creativecommons.org/licenses/by/2.5/ca/ Except where otherwise noted, this item's license is described as http://creativecommons.org/licenses/by/2.5/ca/

Search the Atrium


Advanced Search

Browse

My Account