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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.
wavelets, function decomposition, image compression, multiresolution analysis
David H. Salesin, Tony D. DeRose, Eric J. Stollnitz, "Wavelets for Computer Graphics: A Primer, Part 1", IEEE Computer Graphics and Applications, vol. 15, no. , pp. 76-84, May 1995, doi:10.1109/38.376616
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