<Wavelet license plate>

Wavelets in Computer Graphics

Multiresolution techniques and the use of hierarchy have a long history in computer graphics. Most recently these approaches have received a significant boost and increased interest through the introduction of the mathematical framework of wavelets. With their roots in signal processing and harmonic analysis, wavelets have lead to a number of efficient and easy to implement algorithms. Wavelets have already had a major impact in several areas of computer graphics: Some of the very recent and most exciting generalizations and extensions of classical wavelet constructions have been developed by researchers in the context of graphics applications. Following the success of the wavelets courses at SIGGRAPH 94 and 95 and based on the experiences of the organizers and lecturers, there will be another wavelets course at SIGGRAPH 96. Since new wavelet constructions now exist, which are easy to implement and do not require any heavy mathematical machinery to describe, the course will be accessible to those who do not have any prior knowledge of wavelets or a strong background in mathematical Fourier theory.

Course Materials

The course notes themselves come in a number of postscript files The slides for the first (basic) part of the course are also available The images from the slides were all generated with LIFTPACK, a software package for computing wavelet transform using lifting.


The course will run for a whole day and consist of introductory lectures covering wavelet basics as well as advanced lectures describing some state of the art applications in computer graphics.


Morning: Introductory Material - Peter Schröder and Wim Sweldens:

Afternoon: Applications - David Salesin, Tony DeRose, Peter Schröder, Wim Sweldens, Michael Cohen

Contact Info

Peter Schröder Wim Sweldens
Assistant Professor of Computer Science
Computer Science Department 256-80
California Institute of Technology
Pasadena, CA 91125
vox: 818.395.4269
fax: 818.792.4257
net: ps@cs.caltech.edu
Member of Technical Staff
Lucent Technologies, Bell Laboratories
Room 2C-175
700 Mountain Avenue
Murray Hill, NJ 07974
vox: 908.582.3288
fax: 908.582.2379
net: wim@lucent.com

Michael Cohen Tony DeRose David Salesin
Microsoft Research
One Microsoft Way
Redmond, WA 98052
vox: 206.703.0134
fax: 206.936.7329
net: mcohen@microsoft.com
Member of Tools Group
Pixar Animation Studios
1001 West Cutting Blvd.
Richmond, CA 94804
vox: 510.236.4000
fax: 510.236.0388
net: derose@pixar.com
Assistant Professor
Dept. of CS and Engr.
University of Washington
Seattle, WA 98195
vox: 206.685.1227
fax: 206.543.2969
net: salesin@cs.washington.edu

Speaker Biographies

Peter Schröder is an assistant professor of computer science at the California Institute of Technology, Pasadena. He received a BS in mathematics from the Technical University of Berlin in 1987 and his Master degree from the MIT Media Lab in 1990. After working for Thinking Machines Corporation on massively parllel graphics algorithms he studied computer graphics under Pat Hanrahan at Princeton Unviversity and received his PhD in 1994 for research on wavelet based algorithms for illumination computations. Most recently he was a postdoctoral research fellow at the University of South Carolina under the direction of Björn Jawerth.

He has worked extensively in the area of wavelet based methods for many graphics related problems, and made fundamental contributions in this area. His work on the subject has appeared at SIGGRAPH as well as in WIRED magazine and he has lectured widely in Europe and the US on the subject including previous SIGGRAPH courses.

Wim Sweldens is a researcher at the Mathematics Center of Lucent Technologies, Bell Laboratories. (Lucent Technologies is the former systems and technology part of AT&T.) He received his PhD in May 1994 from the Katholieke Universiteit Leuven, Belgium, for his work on wavelet constructions and applications in numerical analysis. Until May 1995 he was a postdoctoral research fellow at the University of South Carolina where he worked with Peter Schröder and Björn Jawerth.

In his PhD dissertation he introduced the notion of ``Second Generation Wavelets,'' a generalization of classical wavelets which allows wavelet transforms for irregularly sampled data and data defined on complex geometries. Later he discovered the ``Lifting Scheme,'' a very general and easy to implement construction of Second Generation Wavelets, which can also be used to introduce wavelets without the use of Fourier analysis. More recently, his work has been concerned with the application of wavelets to computer graphics. He has lectured widely on wavelets and their applications throughout Europe and the United States as well as in two previous SIGGRAPH courses. He is the founder and current editor of the Wavelet Digest, a newsletter on the Internet concerned with wavelets.

Michael F. Cohen is curently a member of the research staff at Microsoft. He came to Microsoft from Princeton University where he was an Assistant Professor of Computer Science. Michael received his PhD in 1992 from the University of Utah. He also holds undergraduate degrees in Art from Beloit College and in Civil Engineering from Rutgers University. He began his career in computer graphics at Cornell University where he received an MS in 1985. Dr. Cohen also served on the Architecture faculty at Cornell University and was an adjunct faculty member at the University of Utah. His recent work has focused on spacetime control for linked figure animation and variational modeling methods. He is perhaps better known for his work on the radiosity method for realistic image synthesis as discussed in his recent book ``Radiosity and Image Synthesis'' (co-authored by John R. Wallace). His current interests range from linked figure animation, to image capture and synthesis, to intelligent camera control, and image based rendering. Michael has published widely and presented his work internationally in these and other areas.

Tony DeRose is currently a member of the Tools Group at Pixar Animation Studios. He received a BS in Physics in 1981 from the University of California, Davis; in 1985 he received a Ph.D. in Computer Science from the University of California, Berkeley. He received a Presidential Young Investigator award from the National Science Foundation in 1989. In 1995 he was selected as a finalist in the software category of the Discover Awards.

From September 1986 to December 1995 Dr. DeRose was a Professor of Computer Science and Engineering at the University of Washington. From September 1991 to August 1992 he was on sabbatical leave at the Xerox Palo Alto Research Center and at Apple Computer. He has served on various technical program committees including SIGGRAPH, and from 1988 through 1994 was an associate editor of ACM Transactions on Graphics.

His research has focused on mathematical methods for surface modeling, data fitting, and more recently, in the use of multiresolution techniques. Recent projects include surface reconstruction from laser range data and multiresolution/wavelet methods for high-performance computer graphics.

David Salesin teaches Computer Science and Engineering at the University of Washington, Seattle, where he has recently been promoted to Associate Professor. He received his ScB from Brown University in 1983, his PhD from Stanford University in 1991, and joined the faculty at the University of Washington in the fall of that year. From 1983-86, he worked at Lucasfilm, where he contributed computer animation for the Academy Award-winning short film, ``Tin Toy,'' and the feature-length film Young Sherlock Holmes. He spent the 1991-92 year on leave as a Visiting Assistant Professor in the Program of Computer Graphics at Cornell University. In 1993, he received an NSF Young Investigator award. In 1995, he received an ONR Young Investigator Award and was named an Alfred P. Sloan Research Fellow and an NSF Presidential Faculty Fellow.

Professor Salesin's research interests are in computer graphics, and include photorealistic image synthesis and computer-generated illustration in particular. He has had a major impact on the use of wavelets in computer graphics and is co-author (with Eric Stollnitz and Tony DeRose) of the forthcoming book ``Wavelets for Computer Graphics'' (Morgan-Kaufman).

Summary Statement

The course is designed to introduce practitioners in the field of computer graphics to the many applications of wavelets: multiresolution curve and surface modeling, image compression and processing, radiosity and radiance computations, solution of PDEs, and constrained optimization problems. It covers both wavelet fundamentals and application driven algorithms, which can be put to immediate use by the participants. Applications and algorithmic implementation details will be emphasized.

Course Level

Intermediate The course is self contained and participants are not expected to have prior knowledge of wavelets. Familiarity with basic questions of computer graphics research is assumed.

Course Objectives

The course aims to give participants a working knowledge of wavelets and their fundamental algorithms. It will provide enough basics to serve as a starting point for independent evaluation of the presented, as well as future techniques. In the first half the focus is on the basic techniques: one dimensional and higher dimensional forward and inverse transforms; different wavelets and their various tradeoffs; general and simple construction tools for a large class of wavelets, applicable in many different settings, including arbitrary curves, surfaces and volumes; fundamental processing algorithms such as smoothing, denoising, compression, and non-linear approximation. Intuitive examples will be used throughout to motivate and introduce all techniques. The aim is to make it possible for participants to immediately implement the discussed algorithms. In the second half of the course participants will learn about the algorithmic details of the major applications of wavelets in graphics. Again the focus will be on ``making things work'' for real world applications. This is necessarily done at a somewhat higher level, but with the basics from the first half the participants will be able to envision every step along the way to a successful implementation. In general we will emphasize algorithmic ``know how'' and its efficient realization in real world applications over mathematical analysis. For the latter interested readers will find extensive notes and pointers to the literature in the course materials. After the course participants will be able to confidently evaluate the suitability of wavelets for various application contexts, and rapidly implement custom designed wavelets wherever applicable.

Course Prerequisites

Basic college level linear algebra and calculus will be assumed. Familiarity with fundamental computer graphics algorithms and techniques is helpful to motivate and put into perspective, many of the taught techniques.

Intended Audience

The course is aimed at practitioners - students, researchers, implementors - in the field of computer graphics who want to come up to speed rapidly on this important new set of tools, as well as people already familiar with wavelets who want to find out about the current state of the art.

Course Notes Description

The course notes will follow the basic syllabus outline given above. The first half will be co-written by the organizers, to guarantee a comprehensive and continuous treatment of all the basic foundations. The structure of the presentation will be hierarchical: examples will be interspersed throughout to motivate and explain basic ideas. Sections with deeper material, suitable for skipping on a first pass, will be so marked. With these foundations in place the second half will consist of topic treatments from the latest research of some of the major contributors to this area of graphics. In second part the emphasis will be on the application of the fundamental techniques taught in the first part to the construction of ``industrial strength'' applications.

Special Notes Requirements

The CDROM will contain ready to run code for the basic techniques presented in the course.

Copyright © 1996 Peter Schröder and Wim Sweldens