filename     : 220
entry        : techreport

number       : 220
pages        : 24
year         : 1994
title        : A New Method to Approximate the Volume Rendering Equation using Wavelet Bases and Piecewise Polynomials
entry        : techreport
author       : M. Gross and L. Lippert and A. Dreger and R. Koch
month        : Sep
address      : Institute of Inofmation Systems
institution  : ETH Zürich
abstract     :
In this paper we describe a new generic method to find an approximate
solution for the volume rendering equation using hierarchical, orthonormal 
wavelet basis functions. The approach is based on the idea that an initial 
volume data set can be decomposed into a pyramidal representation by means 
of a 3D wavelet transform. Once the wavelet function is described analytically,
it is possible to approximate the volume density function. Moreover, when 
employing piecewise polynomial spline functions, as in our method, the
rendering integral can also be approximated and gradient functions or related 
features of the data can be computed immediately from the approximation.
Due to the localization properies of the wavelet transform both in space and 
in frequency on the one side and due to the pyramidal subband coding scheme on 
the other side, this technique allows additionally for the control of the local
quality of the reconstruction and provides elegantly for level-of-detail 
operations.
Aside from the solution of the rendering equation itself, isosurfaces of the 
data can also be computed with either standard techniques, like marching cubes,
or by more sophisticated algorithms that render the basis functions. All these 
additional rendering techniques can be embedded in a hybrid surface/volume 
rendering scheme. In our paper, we elucidate this new concept and show its 
capabilities by different examples.