Graphics Reference
In-Depth Information
The ray-casting technique has become the most common method used for
real-time rendering of volume data. This may seem surprising, because ray tracing
has a reputation of being too slow for real-time rendering. However, ray tracing
is slow for surface rendering because of the cost of computing ray intersections.
Ray/voxel intersections are much simpler because of the regular placement of the
voxels and the simplicity of intersecting a cube with a ray.
3.2.2 History of Volume Rendering
The emergence of computed tomography (CT) in the 1970s was a driving force
behind volume data visualization research in the medical field. CT data is ob-
tained from a scanning machine that records absorption of X-rays fired from a
rotating emitter. The scan proceeds along an axis perpendicular to the plane of
rotation so that the data consists of cross-sectional “slices” of a human body (or
whatever object is being scanned). The result is a collection of tissue-density data
distributed in a volume. Different types of tissue have different densities: air, soft
tissue, fat, and bone can be distinguished in CT data..
Changes in density—boundaries between a region of identical or similar den-
sity and a region of a different density—correspond to the surfaces of internal
objects. Known as
isosurfaces
, these are the 3D analogue of contour lines on a
2D plot. The problem of how to render or “image” isosurfaces is part of volume
rendering. Early techniques for volume rendering attempted to isolate and render
these isosurfaces using standard surface-rendering techniques.
The
marching cubes
algorithm is an established technique for isosurface vi-
sualization. It was originally presented in a 1987 paper by William E. Lorensen
and Harvey E. Cline [Lorensen and Cline 87]. The marching cubes algorithm
is voxel based. It works by approximating the isosurface inside each voxel as a
plane, which becomes a polygon when restricted to the voxel, and this becomes
a facet of the computed isosurface representation. The surface is constructed by
starting at one end of the voxel grid and “marching” along the grid in one di-
mension, connecting the facets in each section with those of the previous section.
The resulting isosurfaces are piecewise polygonal and are limited to the precision
of the voxel grid. One drawback to marching cubes for medical imaging comes
from the “all-or-nothing” assumption that the surface is strictly bounded by the
plane in the voxel. Surfaces in a CT data set are often fuzzier; the all-or-nothing
assumption can produce noticeable artifacts in the final image.
In 1988, a year after the marching cubes paper was published, Marc Levoy
introduced a fundamentally different technique for rendering isosurfaces based
on the data points only, without explicit surface reconstruction [Levoy 88]. The
