A new method to approximate the volume rendering equation using wavelet bases and piecewise polynomials
Gross, Markus H.
Rights / licenseIn Copyright - Non-Commercial Use Permitted
In the following 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 Show more
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Journal / seriesETH, Eidgenössische Technische Hochschule Zürich, Departement Informatik, Institut für Informationssysteme
PublisherDepartement Informatik, ETH
SubjectVOLUMENWIEDERGABE (NUMERISCHE MATHEMATIK); OBJEKTMODELLIERUNG (COMPUTERGRAFIK); OBJECT MODELLING (COMPUTER GRAPHICS); PROGRAMS AND ALGORITHMS FOR THE SOLUTION OF SPECIAL PROBLEMS; WAVELETS + WAVELET TRANSFORMATIONS (MATHEMATICAL ANALYSIS); WAVELETS + WAVELET-TRANSFORMATIONEN (ANALYSIS); VOLUME RENDERING (NUMERICAL MATHEMATICS); PROGRAMME UND ALGORITHMEN ZUR LÖSUNG SPEZIELLER PROBLEME
Organisational unit02150 - Dep. Informatik / Dep. of Computer Science
NotesTechnical Reports D-INFK.
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