language: en

[COMPUTER GRAPHICS Proceedings, Annual Conference Series,]

1994

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

Philippe Lacroute
Computer Systems Laboratory Stanford University
Marc Levoy
Computer Science Department Stanford University

Abstract 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 with minimal loss of image quality. Shear-warp factorizations have the property that rows of voxels in the volume are aligned with rows of pixels in the intermediate image. We use this fact to construct a scanline-based algorithm that traverses the volume and the intermediate image in synchrony, taking advantage of the spatial coherence present in both. We use spatial data structures based on run-length encoding for both the volume and the intermediate image. Our implementation running on an SGI Indigo workstation renders a 256 3 voxel medical data set in one second. Our second extension is a shear-warp 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. The method extends to support mixed volumes and geometry and is parallelizable.

CR Categories: I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism; I.3.3 [Computer Graphics]: Picture/Image Generation|Display Algorithms. Additional Keywords: Volume rendering, Coherence, Scientific visualization, Medical imaging.

1 Introduction