The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.04 - July (1995 vol.15)
pp: 75-85
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 discussed the simple case of Haar wavelets in one and two dimensions, and showed how they can be used for image compression. Part II presents the mathematical theory of multiresolution analysis, develops bounded-interval spline wavelets, and describes their use in multiresolution curve and surface editing.
INDEX TERMS
wavelets, multiresolution analysis, spline wavelets, surface editing.
CITATION
Eric J. Stollnitz, Tony D. DeRose, David H. Salesin, "Wavelets for Computer Graphics: A Primer, Part 2", IEEE Computer Graphics and Applications, vol.15, no. 4, pp. 75-85, July 1995, doi:10.1109/38.391497
REFERENCES
1. C.K. Chui, “An Overview of Wavelets,” in Approximation Theory and Functional Analysis, C.K. Chui, ed., Academic Press, Boston, 1991, pp. 47–71.
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. 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, Oct. 1993.
4. E. Quak and N. Weyrich, “Decomposition and Reconstruction Algorithms for Spline Wavelets on a Bounded Interval,” Applied and Computational Harmonic Analysis, Vol. 1, No. 3, June 1994, pp. 217-231.
5. I. Daubechies, “Orthonormal Bases of Compactly Supported Wavelets,” Comm. on Pure and Applied Mathematics, Vol. 41, No. 7, Oct. 1988, pp. 909-996.
6. A. Finkelstein and D.H. Salesin, “Multiresolution Curves,” Siggraph 94 Conf. Proc., ACM, New York, 1994, pp. 261-268.
7. 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.
8. C.K. Chui, An Introduction to Wavelets.Boston: Academic Press, 1992.
9. C.K. Chui and E. Quak, “Wavelets on a Bounded Interval,” in Numerical Methods in Approximation Theory—Vol. 9, D. Braess and L. L. Schumaker, eds., Birkhauser Verlag, Basel, Switzerland, 1992, pp. 53–75.
10. G. Farin, Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide. Academic Press, 1993.
11. R.H. Bartels, J.C. Beatty, and B.A. Barsky, An Introduction to Splines for Use in Computer Graphics and Geometric Modeling, Morgan Kaufmann, Los Altos, Calif., 1987.
12. W.H. Press et al., Numerical Recipes, 2nd ed., Cambridge Univ. Press, 1992.
13. M.P. Salisbury et al., "Interactive Pen-And-Ink Illustration," Proc. Siggraph 94, ACM Press, 1994, pp. 101-108.
14. M. Eck et al., “Multiresolution Analysis of Arbitrary Meshes,” Tech. Report 95-01-02, Univ. of Washington,” Jan. 1995.
15. E.J. Stollnitz, T.D. DeRose, and D.H. Salesin, Wavelets for Computer Graphics: Theory and Applications. Morgan Kaufmann, 1996.
18 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool