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   -> Volume 4, Issue 5

Preprint: A New Method to Approximate the Volume Rendering Equation...
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Lars Lippert

PostPosted: Tue Dec 03, 2002 11:34 am    
Subject: Preprint: A New Method to Approximate the Volume Rendering Equation...
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Preprint: A New Method to Approximate the Volume Rendering Equation...

Title: A New Method to Approximate the Volume
Rendering Equation using Wavelet Bases
and Piecewise Polynomials

Preprint & figures available by anonymous ftp from
Directory: /doc/tech-reports/1994

Report-No: 220

Authors: M. Gross, L. Lippert, A. Dreger, R. Koch

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
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.

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