HOME    »    PROGRAMS/ACTIVITIES    »    Annual Thematic Program
IMA Minisymposium
Fractals in Multimedia
January 17-19, 2001


Organizers:

Michael F. Barnsley
Department of Mathematics and Statistics
University of Melbourne

mbarnsley@aol.com

Edward Vrscay
Department of Applied Mathematics
University of Waterloo

ervrscay@links.uwaterloo.ca

Dietmar Saupe
Institut fur Informatik
Universitaet Leipzig

saupe@informatik.uni-leipzig.de

 

The development of multimedia has often showcased its achievements, in resolution and computing power, by displaying fractal pictures. These pictures of strange attractors and Julia sets have been emblematic of the beauty and depth of mathematics. This mini-symposium will demonstrate, however, that fractals are more than pretty pictures; the underlying mathematics leads to a broad collection of useful mathematical tools, common themes, new ways of looking at and thinking about existing algorithms, and practical applications. The focus will be on the main ideas of fractal mathematics as applied to multimedia, and science, and how they may develop in the future.

Fractal mathematics has developed out of the observation that in the real world and in the scientific measurement of it, there can occur patterns that repeat at different scales. This mathematics consists of some basic tools and theorems, such as IFS theory and Hutchinson's theorem; it is centered in real analysis, geometry, measure theory, dynamical systems, and stochastic processes. Its application to multimedia lies principally in the attempt to bridge the divide between the discrete world of digital representation and the natural continuum world in which we seem to live. It has served as inspiration for algorithms that try to recreate sounds, pictures, motion video, and textures, and to organize databases, in computer environments.

Topics addressed at the mini-symposium will include multimedia video algorithms, lossless fractal compression, resolution enhancement, fractal transform image compression, fractal image recognition, segmentation, space-filling curves, fractal graphics, and fractals in education. The meeting will involve mathematicians, computer scientists, engineers and industrial researchers who are interested in the application of fractal methods. The philosophical basis for the symposium is the set of those intuitions and insights that a fractal perspective brings, and the mathematics that sustains those realizations. It is intended that the various speakers will say what their intuitions are, how they look mathematically, and how they are applied in his or her topic. The conference would try to identify areas where the fractal viewpoint has potential to increase understanding and lead to new algorithms.

MINISYMPOSIUM SCHEDULE

WEDNESDAY, JANUARY 17
All talks are in Lecture Hall EE/CS 3-180 unless otherwise noted.
8:30am Coffee and Registration

Reception Room EE/CS 3-176

9:10 am Willard Miller, Fred Dulles, and Michael F. Barnsley Introduction
Fractals in Education and on the Internet
9:30 am Vicki G. Fegers and Mary Beth Johnson
School Board of Broward County (FL)
Talk  pdf
10:30 am Break Reception Room EE/CS 3-176
11:00 am-12:00 pm Michael Frame
Union College
A Web-Based Fractal Geometry Course for Non-Science Students

URL for the presentation

Fractal Image Compression
1:30 pm Dietmar Saupe
Universitaet Leipzig
The State of the Art in Pure Fractal Compression
2:30 pm Break Reception Room EE/CS 3-176
2:45 pm Raouf Hamzaoui
Universitat Leipzig
Fast Local Search for Fractal Image Compression

Material from Talk   Slides pdf

3:45 pm Break Reception Room EE/CS 3-176
4:00 pm Edward Vrscay
University of Waterloo
From Fractal Image Compression to Fractal-based Methods in Mathematics

Slides

5:00 pm IMA Tea
A variety of appetizers and beverages will be served.
IMA East, 400 Lind Hall
THURSDAY, JANUARY 18
All talks are in Lind Hall 409 unless otherwise noted.
8:45 am Coffee Reception Room, Lind Hall 400
9:00 am Michael F. Barnsley
University of Melbourne
Lossless Fractal Compression Using IFS
10:00-11:00 am John Elton
Georgia Institute of Technology
IFS with Place-Dependent Probabilities
11:00 am Break Reception Room, Lind Hall 400
11:00 am-12:30 pm Doug Hardin
Vanderbilt Univerity
From Fractal Interpolation Functions to Wavelets: The HD Problem for Refinable Functions
Fractal Image Techniques in Multimedia Processing
2:00 pm Jean-Luc Dugelay
Institut EURECOM
Fractals in Multimedia Imaging: From Compression to Image Indexing to Watermarking
3:00 pm Break Reception Room, Lind Hall 400
3:30 pm Ning Lu
Advanced Digital Imaging Laboratories, Inc.
Fractal Techniques in Image Segmentation
4:30-5:30 pm Jacques Levy-Vehel
INRIA, Rocquencourt
TBA
FRIDAY, JANUARY 19
All talks are in Lind Hall 409 unless otherwise noted.
Fractal Graphics, Enhancement and Zoom
8:45 am Coffee Reception Room, Lind Hall 400
9:00 am Ken Musgrave
FractalWorlds.com
Windows on a Parallel Universe: Exploring Fractal Planets
10:00 am Break Reception Room, Lind Hall 400
10:30-11:30 am Lyman P. Hurd
Iterated Systems, Inc.

A Lagrangian Cost Model for a Fractal Transform Compressor

Talk   pdf

11:30 am-12: 30 pm Martin J. Turner
De Montfort University
On the Statistics of Dimension: Multi-fractalsand Fractal Modulation

Related Papers: imapapjmb.pdf (949KB)  imapapjmb.ps (32.6MB)  imapapjmb.ps.gz (1.4MB)  papifs.pdf (4MB)  papifs.ps (26KB)  papifs.ps.gz (5.7MB)  

12:30 pm IMA Lunchtime Movie "Is God a Number?"
Fractal Image Compression II : The Future
2:00 - 3:30 pm

Panel Discussion on Fractal Image Compression

2:00-2:15 pm Dietmar Saupe, Universitaet Leipzig
2:15-2:30 pm John Elton, Georgia Institute of Technology
2:30-2:45 pm Ning Lu, Advanced Digital Imaging Laboratories, Inc.
2:45- 3:00 pm Michael F. Barnsley, University of Melbourne
3:00- 3:30 pm Q&A and Discussion
3:00 pm Break Reception Room, Lind Hall 400
4:00 pm Franklin Mendivil
Acadia University

Fractal Vector-Measures on Fractals

Talk   pdf    postscript

5:00-5:30 pm Herb Kunze
University of Guelph

Using the Picard Contraction Mapping to Solve Problems in ODEs

Talk    pdf


LIST OF CONFIRMED PARTICIPANTS

(in addition to postdocs and long term participants)

as of 1/18/2001
Name Department Affiliation
Simon Alexander Applied Mathematics University of Waterloo
Michael Barnsley Mathematics & Statistics University of Melbourne
Eugene Belogay Honors College, FAU 5353 Parkside Dr.
Santiago Betelu   Institute for Mathematics and its Applications
Jamylle Carter   Institute for Mathematics and its Applications
Barry Cipra    
Steven Demko   Iterated Systems, Inc.
Jean-Luc Dugelay Multimedia Communications Institut EURECOM
Fred Dulles   Institute for Mathematics & its Applications
John Elton Mathematics Georgia Institute of Technology
Selim Esedoglu   Institute for Mathematics and its Applications
Vicki Fegers Program Development and Alignment School Board of Broward County, FL
Michael Frame Mathematics Union College
Robert Gulliver Mathematics University of Minnesota
Raouf Hamzaoui Inst. fur Informatik Universitat Leipzig
Bin Han   Institute for Mathematics and its Applications
Doug Hardin Mathematics Vanderbilt University
Lyman Hurd MediaBin Iterated Systems, Inc.
Mary Beth Johnson Program Development and Alignment School Board of Broward County, Florida
Herb E. Kunze Math & Stats University of Guelph
Instructor Kevin Lee Mathematic/Computer Science Normandale Community College
Jaques Levy-Vehel   INRIA, Rocquencourt
Ning Lu   Advanced Digital Imaging Laboratories, Inc.
Franklin Mendivil Math Acadia University
Willard Miller   Institute for Mathematics & its Applications
Ken Musgrave   FractalWorlds.com
Jianliang Qian   Institute for Mathematics and its Applications
Dietmar Saupe Institut fur informatik Universitaet Leipzig
Cheri Shakiban   University of St. Thomas
Martin J. Turner Institute of Simulation Sciences De Montfort University
Edward Vrscay Applied Mathematics University of Waterloo
Ruifeng Xie   Iterated Systems, Inc.


Talk Abstracts

2000-2001 Program: Mathematics in Multimedia

Back to top of page

Go