Wavelets for computer graphics: a primer.1

Abstract

Wavelets are a mathematical tool for hierarchically decomposing functions. They allow a function to 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 offer an elegant technique for representing the levels of detail present. The article is intended to provide people 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. We discuss the simple case of Haar wavelets in one and two dimensions, and show how they can be used for image compression.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>