Fast Volume Rendering Using a Shear-Warp Factorization of the Viewing Transformation

Philippe Lacroute, Ph.D. dissertation, Technical Report CSL-TR-95-678, Stanford University, 1995.


Volume rendering is a technique for visualizing 3D arrays of sampled data. It has applications in areas such as medical imaging and scientific visualization, but its use has been limited by its high computational expense. Early implementations of volume rendering used brute-force techniques that require on the order of 100 seconds to render typical data sets on a workstation. Algorithms with optimizations that exploit coherence in the data have reduced rendering times to the range of ten seconds but are still not fast enough for interactive visualization applications. In this thesis we present a family of volume rendering algorithms that reduces rendering times to one second.

First we present a scanline-order volume rendering algorithm that exploits coherence in both the volume data and the image. We show that scanline-order algorithms are fundamentally more efficient than commonly-used ray casting algorithms because the latter must perform analytic geometry calculations (e.g. intersecting rays with axis-aligned boxes). The new scanline-order algorithm simply streams through the volume and the image in storage order. We describe variants of the algorithm for both parallel and perspective projections and a multiprocessor implementation that achieves frame rates of over 10 Hz.

Second we present a solution to a limitation of existing volume rendering algorithms that use coherence accelerations: they require an expensive preprocessing step every time the volume is classified (i.e. when opacities are assigned to the samples), thereby limiting the usefulness of the algorithms for interactive applications. We introduce a data structure for encoding spatial coherence in unclassified volumes. When combined with our rendering algorithm this data structure allows us to build a fully-interactive volume visualization system.

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