Wavelets for Computer Graphics

Overview

Wavelets are a mathematical tool for hierarchically decomposing functions. They allow any function to be described in terms of a coarse overall shape, plus details that range from broad to narrow. As the figures below illustrate, wavelets can be applied to a wide variety of objects used in graphics, including images, curves, surfaces, and the solutions to lighting simulations.

Images
20 coefficients
200 coefficients
16,000 coefficients
Curves
level 3.1
level 5.4
level 8.0
Surfaces
229 triangles
2,000 triangles
10,000 triangles
Simulation
no refinement
6 refinements
final gather

Publications

Although a great deal has been written about wavelets, most of the literature uses terminology from signal processing and pure mathematics. Our aim in writing the tutorial article and the book listed below was to provide a consistent theoretical framework for those working in computer graphics, as well as examples of graphics applications that make use of wavelets.

Article
The Article

 Wavelets for Computer Graphics: A Primer. Eric J. Stollnitz, Tony D. DeRose, and David H. Salesin. IEEE Computer Graphics and Applications, 15(3):76-84, May 1995 (part 1), and 15(4):75-85, July 1995 (part 2).
Book
The Book

 Wavelets for Computer Graphics: Theory and Applications. Eric J. Stollnitz, Tony D. DeRose, and David H. Salesin. Morgan Kaufmann, San Francisco, 1996.
Matlab
Matlab

 Matlab code used to generate endpoint-interpolating B-spline wavelet matrices and figures for the book and the IEEE CG&A article.

The Authors

Eric
Eric Stollnitz		 Tony
Tony DeRose		 David
David Salesin

Related Work

Here's a list of other publications involving wavelets and graphics, all by members of the University of Washington's graphics group.

More coprehensive information about wavelets can be obtained from Wavelet Digest and MathSoft's Wavelet Resources.

<stoll@amath.washington.edu> 4:01 pm, 1 October 1998