This volume describes the status of
fractal imaging
research and looks to
future directions. It will be useful
to researchers in the
areas of fractal image compression,
analysis, and synthesis, iterated function systems, and
fractals in education. In particular it includes a vision
for the future of these areas. It is intended to provide an
efficient means by which researchers can look back over the
last decade at what has been achieved, and look forward
towards second-generation fractal imaging. The chapters in
themselves are not meant to be detailed reviews or
expositions, but to serve as signposts to the state of the
art in their areas. What is important is what they mention
and what tools and ideas are seen now to be relevant to the
future. The contributors, a number of whom have been
involved since the start, are active in fractal imaging,
and provide a well-informed viewpoint on both the status
and the future. Most were invited participants at a meeting
on "Fractals in Multimedia" held at the IMA in January
2001. Some goals of the minisymposium, shared with this
volume, were to demonstrate that the fractal viewpoint
leads to a broad collection of useful mathematical tools,
common themes, new ways of looking at and thinking about
existing algorithms and applications in multimedia, and to
consider future developments.We try to further define the
set of those intuitions and insights that constitute the
fractal viewpoint, the mathematics that sustains it, and to
identify areas where it has potential to increase
understanding and lead to new discoveries.Whom this book is
for:
This book should be useful to commercial and university
researchers in the rapidly evolving field of digital
imaging, specifically, chief information officers,
professors, software engineers, and graduate students in
the mathematical sciences. While much of the content is
quite technical, it contains pointers to the
state-of-the-art and the future in fractal
imaging.
Contents
- Introduction to IMA fractal proceedings
- Uniqueness of invariant measures for place-dependent
random iterations of functions
- Iterated function systems for lossless data
compression
- From fractal image compression to fractal-based methods
in mathematics
- Fractal image compression with fast local search
- Wavelets are piecewise fractal interpolation
functions
- Self-affine vector measures and vector calculus on
fractals
- Using the Picard contraction mapping to solve inverse
problems in ordinary differential equations
- Fractal modulation and other applications from a theory
of the statistics of dimension
- Signal enhancement based on Hoelder regularity
analysis
- Iterated data mining techniques on embedded vector
modeling
- A web-based fractal geometry course for non-science
students
- List of minisymposium participants