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density of the substance and the percentage contained in the voxel. A boundary
occurs when there is a sharp change in this density, which can be detected by
examining the gradient (differential rate of change) of the density. The gradient
is a 3D vector that is large in magnitude when there is a sharp transition between
materials of different densities. Away from a surface the density variation is small,
and so is the gradient. The magnitude of the gradient, described as the “surface
strength,” serves to estimate the amount of surface present. The direction of the
gradient is perpendicular to the boundary surface. The surface strength plays an
important role in the process of color computation.
The color computation depends on the color properties in three regions in a
voxel: the region in front of the surface, the region behind the surface, and a thin
region corresponding to the surface itself. Each region has a color and an opacity,
and can also emit light. Light passing through a voxel is colored by a composition
of the colors in the three regions; opacity is included, but attenuation inside the
voxel is not.
The color produced by light reflection from the implied surface is computed
much as in surface rendering, i.e., as a function of the viewpoint, the surface nor-
mal, and the light source. The surface shading is split into a diffuse and specular
component: the diffuse component comes from the color of the surface; the specu-
lar component, from the color of the light source. The diffuse surface color is that
of the region behind the surface, which prevents color bleeding between neigh-
boring materials. An additional step not applied in normal surface rendering is to
scale the final color by the strength of the surface. A voxel that contains no sur-
face has a surface strength of (nearly) zero, so the surface reflectance contribution
is very small. The appearance of the surface so rendered therefore depends on the
gradient, which depends on the density. The algorithm ensures the continuity of
the data at each step, so the method produces the appearance of a smooth surface
without actually reconstructing the surface geometry.
The final image is constructed by first using fast image-warping techniques
to transform each of the two-dimensional slices of the volume into the viewing
coordinate system so that voxel boundaries are parallel to view rays. Projection
onto the image plane then amounts to compositing the sequential run of voxels
corresponding to each pixel. The density and gradient computation can actually
be done independently in each slice of CT data, and if the viewpoint is placed at
“infinity,” perpendicular to the slice planes, no transformation is necessary. This
is another feature of the method.
The volume visualization algorithm described in the paper assumes the ma-
terial percentages for each voxel are available from the data set. The paper
also contains an algorithm for classifying measured CT data, which is composed
purely of X-ray absorption values, into separate substances.
It works using a
