Biomedical Engineering Reference
In-Depth Information
produce the desired rendering may be greater than the
data points can support. In such cases, interpolation
becomes the single major factor that can determine
the quality of the rendered image. More elaborate in-
terpolation techniques can take into account not just
eight surrounding data points but the 26 neighboring cells
to compute a cubic polynomial interpolation. Such in-
terpolation techniques give very good results, but the
additional speed penalty may be quite high. When the
original volume of data is fairly large ( > 256 256 64),
trilinear interpolation may provide good results to fulfill
many visualization purposes.
gradient in the scalar 3D field data. The gradient vector
was estimated using the gradient along the three princi-
pal axes of the volume or the 26 neighbors.
Lighting effects are particularly useful with CT image
data where the surface features in the data are well
pronounced because of the limited number of features
that CT imaging resolves. However, with MR images,
lighting does not always produce better results. Its con-
tributions depend on the data contrast and noise. Noise
in the data can affect gradient calculation much more
strongly than the linear interpolation estimations.
Transfer functions
The hidden difficulty of volume rendering resides in the
weighting factor of the accumulation equations. The
weighting factor or the opacity value can be assigned for
different data points in the volume to enhance or suppress
their influence in the rendered image. The transfer func-
tion or the lookup table for the weighting factor serve this
purpose. Since the data points are usually represented as
discrete data of 8,12, or 16 bits, such table sizes are not
very large. However, for floating-point representation of
the data, a transfer function (a piecewise linear or
a continuous polynomial representation) can be used.
Although the transfer function provides considerable
flexibility for controlling transparency or opacity, it may
be sometimes very difficult to enhance the feature of
interest that the user wants to visualize. A small change in
the transfer function may cause large differences in the
final image because many interpolated samples are ren-
dered along each ray, and this large accumulation can
produce oversaturation or under-representation in the
computations. Many automatic approaches to compute
the transfer functions have been proposed, but none have
become popular enough. Hardware-accelerated volume
rendering [29-32] and dramatic improvements in the
speed of computing and graphic systems led to the de-
velopment of interactive approaches where the user
could quickly see the result of the selected transfer
function to determine to the desired one. However,
a highly intelligent transfer function technique that can
operate with minimal user interaction is critical for
a wider clinical acceptance of volume rendering. Alter-
natively, more versatile rendering techniques that do
not depend on sensitive input parameters may also be
developed.
Lighting and shading
One of the important benefits of surface rendering
compared to volume rendering is the lighting and shading
effects that can improve visual cues in the 2D displayed
image. This is figuratively called 2.5D image. Thus, the
lack of lighting in the early volume-rendering models and
in MIP represented a notable drawback. Lighting calcu-
lations were introduced in the blending equations in-
troducing a weighting factor that represented the local
Shell rendering
Many techniques were investigated soon after the
shortcomings of volume-rendering and surface-rendering
techniques were realized. Notable among them is a shell
rendering technique [20] where the general principle is
to combine the strengths of surface rendering and
volume rendering and suppress their weakness. Surface
rendering is very selective in extracting particular
Figure 6.6-5 Multiple projection 2D photographs, back projected
onto the surface obtained from CT and fused with MR of the brain.
(Image courtesy of M. Solaiyappan, Nick Bryan, Pheng Ann Heng.)
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