Philippe Lacroute and Marc Levoy, Fast Volume Rendering Using a Shear-Warp Factorization of the Viewing Transformation, Proc. SIGGRAPH '94, Orlando, Florida, July, 1994, pp. 451-458.


Several existing volume rendering algorithms operate by factoring the viewing transformation into a 3D shear parallel to the data slices, a projection to form an intermediate but distorted image, and a 2D warp to form an undistorted final image. We extend this class of algorithms in three ways. First, we describe a new object-order rendering algorithm based on the factorization that is significantly faster than published algorithms without loss of image quality. The algorithm achieves its speed by exploiting coherence in the volume data and the intermediate image. The shear-warp factorization permits us to traverse both the volume and the intermediate image data structures in synchrony during rendering, using both types of coherence to reduce work. Our implementation running on an SGI Indigo workstation renders a 256^3 voxel medical data set in one second. Our second extension is a derivation of the factorization for perspective viewing transformations, and we show how our rendering algorithm can support this extension. Third, we introduce a data structure for encoding spatial coherence in unclassified volumes (i.e. scalar fields with no precomputed opacity). When combined with our shear-warp rendering algorithm this data structure allows us to classify and render a 256^3 voxel volume in three seconds. Our algorithms employ run-length encoding, min-max pyramids, and multi-dimensional summed area tables. The method extends readily to support mixed volumes and geometry.

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