An Introduction to Wavelets for Scientific Visualization

This paper gives an introduction to wavelet techniques in the context of Scientific Visualization. Wavelets are a powerful tool for the representation of large and complex data sets. Some restrictions apply on the type of data sets which can be represented by wavelets. These restrictions are described in a first part. Thereafter, the basic concepts of wavelet representations are explained: level of detail spaces, wavelet spaces, decomposition and reconstruction algorithms. Orthogonality properties of wavelets and their relations with the ability of computing best approximations are the subject of the next part. Usual applications of wavelet representations in Scientific Visualization are then reviewed. These include progressive transmission, LOD visualization, local area zooming. The last part is dedicated to a recent generalization of wavelet techniques that deals with some types of data sets that cannot be tackle by usual wavelet representations due to the restrictions described in the first part.