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. / The Natural Sciences and Engineering Research Council and the University of Guelph helped to provide financial support for this research.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:OGU.10214/3634 |
| Date | 14 May 2012 |
| Creators | Demers, Matthew |
| Contributors | Kunze, Herb, La Torre, Davide |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Rights | http://creativecommons.org/licenses/by/2.5/ca/ |
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