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.
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 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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