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   -> Volume 4, Issue 7


Meeting: Siggraph 95 Wavelet course
 
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Alain Fournier (fournier@cs.ubc.ca)
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PostPosted: Thu Jan 30, 2003 9:57 am    
Subject: Meeting: Siggraph 95 Wavelet course
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Meeting: Siggraph 95 Wavelet course

SIGGRAPH 95

Wavelets and Their Applications in Computer Graphics

Date: Monday August 6 (Full day)

Course syllabus

In the past few years wavelets have been developed both as a new
analytic tool in mathematics and as a powerful set of practical
tools
for many applications from differential equations to image processing.
Wavelets and wavelets transforms are important to researchers
and practitioners in computer graphics because they are a natural
step from classic Fourier techniques in image processing, filtering
and reconstruction, but also because they hold promises in shape
and light modelling as well.
It is clear that wavelets and wavelet transforms can become as
important and ubiquitous in computer graphics as spline-based technique
are now.

This course is intented to give the necessary mathematical background
on wavelets, and explore the main applications, both current and
potential, to computer graphics. The emphasis is put on the connection between
wavelets and the tools and concepts which should be familiar to
any skilled computer graphics person: Fourier techniques, pyramidal
schemes, spline representations.

- Introduction

Scale and Frequency
Scale: Playing with the pyramid
Frequency: Fourier analysis
Limitations of global transforms
Windowed Fourier Transforms
Continuous Wavelet Transforms
From Continuous to Discrete
Image Pyramids revisited
Haar Transform as a Case Study
Multi-dimensional Wavelets

- Mathematical Properties and Formulations of Wavelets

Dyadic and Discrete Wavelet Transforms
Multiresolution Analysis
Orthogonality and Bi-orthogonality
Approximation Properties
Constructing a Wavelet Basis
Daubechies and Spline (Battle-Lemarie) wavelets

- Image Processing Applications

Signal Compression
Multiscale Edge Detection and Reconstruction
Time vs Space vs Direction
Painting with wavelets

- Curve and Surface Modelling

Properties for Curve and Surface representation
Building the right wavelet
Multiresolution curve representation
Multiresolution Surface representation
Curve and Surface Design with Wavelets

- Wavelet Projections

Projection Methods
Operators on Wavelet Basis
Application to Radiosity Solutions

- Other Applications and Conclusions

Light Flux Representation with Wavelets
Solving Differential and Integral Equations
Fractals and Wavelets
Future Trends

- Discussion and Conclusions

Course Lecturers

Michael Cohen is currently at Microsoft. He was previously Assistant
Professor at the Department of Computer Science at Princeton
University. He is one of the originators of the radiosity approach for
global illumination. He has used in his own research wavelet
techniques for curve modelling and hierarchical space-time control.
email address: mfc@CS.Princeton.EDU

Tony DeRose is Associate Professor at the Department of Computer
Science at the University of Washington. His main research interests
are computer aided design of curves and surfaces, and he has applied
wavelet techniques in particular to multiresolution representation of
surfaces. email address: derose@cs.washington.edu

Michael Lounsbery did his PhD at the University of Washington under
the supervision of Tony DeRose, where he developed techniques for the
multiresolution analysis for surfaces of arbitrary topological type.
email address: louns@cs.washington.edu

Alain Fournier is a Professor in the Department of Computer Science at
the University of British Columbia. His research interests include
modelling of natural phenomena, filtering and illumination models.
His interest in wavelets derived from their use to represent light
flux and to compute local illumination within a global illumination
algorithm he is currently developing. email address:
fournier@cs.ubc.ca

Leena-Maija Reissell is a Research Associate in Computer Science at
UBC, on leave from XOX Corporation, Minneapolis, Minnesota. Ms
Reissell is currently conducting research in curve and surface
approximation with wavelet bases. email address: reissell@cs.ubc.ca

Peter Schröder completed his doctoral studies in Computer Science
at Princeton University. His research activities have included dynamic
modelling for computer animation, massively parallel graphics
algorithms, global illumination algorithms, and most recently the
application of wavelets to hierarchical radiosity algorithms. He has
currently a Post Doctoral position at the University of South Carolina
in Columbia. email address: ps@math.sc.edu

Wim Sweldens is a Research Assistant of the Belgian National Science
Foundation at the Department of Computer Science of the Katholieke
Universiteit Leuven, and a Research Fellow at the Department of
Mathematics of the University of South Carolina. His research
interests include the construction of second generation wavelets and
their applications in numerical analysis and image processing. email
address: sweldens@math.sc.edu

Summary statement

This course is intented to give the necessary mathematical background
on wavelets, and explore the main applications, both current and
potential, to computer graphics. The emphasis is put on the connection
between wavelets and the tools and concepts which should be familiar
to any skilled computer graphics person: Fourier techniques, pyramidal
schemes, spline representations, solution of linear systems.

Course objectives

The immediate objective of the course is to provide enough background
on wavelets so that a researcher or skilled practitioner in computer
graphics can understand the nature and properties of wavelets, and
assess their suitability to solve specific problems in computer
graphics. To achieve this, we will use the natural connections
between wavelets and many techniques familiar in computer graphics. We
will as well describe and analyse current applications. After the
course the attendees should be able to access the basic mathematical
literature on wavelets, understand and review critically the current
computer graphics literature using them, and have some intuition about
the pluses and minuses of wavelets and wavelet transform for a
particular application with which they are familiar.

Course prerequisites

General knowledge of computer graphics is necessary. A good background
in signal or image processing will help. You should be fine if you are
familiar with at least two of the following topics: Fourier
transforms, image pyramids, MIP maps, NIL maps, vector spaces, solving
systems of linear equations.

Intended audience

Researchers and advanced practitioners in computer graphics, who are
currently trying to solve problems in image representation and
compression, curve and surface representation, light representation
and propagation, shading and illumination models.


We will again include basic software with the course, the UBC Wavelets
library written by Bob Lewis, based on last year's issue, but enlarged
and improved.
All times are GMT + 1 Hour
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