The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.03 - May (1995 vol.15)
pp: 76-84
ABSTRACT
Wavelets are a mathematical tool for hierarchically decomposing functions. Using wavelets, a function can be described in terms of a coarse overall shape, plus details that range from broad to narrow. Regardless of whether the function of interest is an image, a curve, or a surface, wavelets provide an elegant technique for representing the levels of detail present. This primer is intended to provide those working in computer graphics with some intuition for what wavelets are, as well as to present the mathematical foundations necessary for studying and using them. In Part I, we discuss the simple case of Haar wavelets in one and two dimensions, and show how they can be used for image compression. Part II will present the mathematical theory of multiresolution analysis, develop bounded-interval spline wavelets, and describe their use in multiresolution curve and surface editing.
INDEX TERMS
wavelets, function decomposition, image compression, multiresolution analysis
CITATION
Tony D. DeRose, Eric J. Stollnitz, "Wavelets for Computer Graphics: A Primer, Part 1", IEEE Computer Graphics and Applications, vol.15, no. 3, pp. 76-84, May 1995, doi:10.1109/38.376616
REFERENCES
1. I. Daubechies, “Orthonormal Bases of Compactly Supported Wavelets,” Comm. on Pure and Applied Mathematics, Vol. 41, 1988, pp. 909-996.
2. S.G. Mallat,“A theory for multiresolution signal decomposition: The wavelet representation,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, no. 7, pp. 674-693, 1989.
3. D. Berman, J. Bartell, and D. Salesin, “Multiresolution Painting and Compositing,” Siggraph 94 Conf. Proc., ACM, New York, pp. 85-90.
4. R.A. DeVore, B. Jawerth, and B.J. Lucier, “Image Compression through Wavelet Transform Coding,” IEEE Trans. Information Theory, vol. 38, no. 2 (Part II)), pp. 719-746, 1992.
5. C.E. Jacobs and A. Finkelstein, S.H. Salesin, “Fast Multiresolution Image Querying,” Proc. SIGGRAPH, 1995.
6. A. Finkelstein and D.H. Salesin, “Multiresolution Curves,” Siggraph 94 Conf. Proc., ACM, New York, 1994, pp. 261-268.
7. S.J. Gortler and M.F. Cohen, "Hierarchical and Variational Geometric Modeling with Wavelets," Symp. Interactive 3D Graphics, pp. 35-42, 1995.
8. M. Lounsbery, T. DeRose, and J. Warren, “Multiresolution Surfaces of Arbitrary Topological Type,” Tech. Report 93-10-05B, Univ. of Washington, Dept. of Computer Science and Engineering, Seattle, Wash., Oct. 1993.
9. D. Meyers, “Multiresolution Tiling,” Computer Graphics Forum, Vol. 13, No. 5, Dec. 1994, pp. 325-340.
10. Z. Liu, S.J. Gortler, and M.F. Cohen, "Hierarchical Spacetime Control," Proc. Annual Conf. Series ACM Siggraph, ACM Press, New York, 1994, pp. 35-42.
11. P.H. Christensen et al., “Clustering for Glossy Global Illumination,” Tech. Report 95-01-07, Univ. of Washington, Dept. of CS and Eng., Seattle, Wash., Jan. 1995.
12. P.H. Christensen et al., “Wavelet Radiance,” Proc. Fifth Eurographics Workshop on Rendering, held in Darmstadt, Germany, 1994, pp. 287-302.
13. S.J. Gortler, P. Schroder, M.F. Cohen, and P. Hanrahan, "Wavelet Radiosity," Computer Graphics Proc., Ann. Conf. Series: SIGGRAPH '93,Anaheim, Calif., pp. 221-230, Aug. 1993.
14. P. Schröder et al., “Wavelet Projections for Radiosity,” Proc. Fourth Eurographics Workshop on Rendering, held in Paris, 1993, pp. 105-114.
15. E.J. Stollnitz, T.D. DeRose, and D.H. Salesin, Wavelets for Computer Graphics, to be published by Morgan-Kaufmann, Palo Alto, Calif., 1995.
16. G. Beylkin, R. Coifman, and V. Rokhlin, “Fast Wavelet Transforms and Numerical Algorithms, Part I,” Comm. on Pure and Applied Mathematics, Vol. 44, 1991, pp. 141-183.
20 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool