Wavelets for computer graphics: a primer, part 2

IEEE Computer Graphics and Applications

Published July 1, 1995

Eric Stollnitz, Tony D DeRose, David H Salesin, Stollnitz

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.

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Research Area:  Graphics (2D & 3D)