Biomedical Engineering Reference
In-Depth Information
this context, it may be justified to say that the routine use
of clinical visualization is waiting for a smart visualization
system that can quickly determine the main interest of
the user and present this information in a convenient
manner. Unlike ID and 2D systems, which appear to
have gained quick clinical entry, 3D systems are still used
primarily in clinical research programs rather than rou-
tine clinical applications. The cost of 3D visualization
systems that can be considered clinically useful is also
relatively high, because of demanding volumetric com-
putations that require very fast systems.
significantly reduced. Reduction can be obtained with
Delaunay triangulation, also known as thin-plate tech-
niques, where coalescing can be extended to include
triangles that are approximately coplanar, within a given
tolerance. This can reduce the triangle population at the
expense of a negligible drop in quality.
Deformable surfaces, balloons, shrink-wrap surface
Surface extraction proves to be very effective when the
signal-to-noise ratio of the data is high and structures are
well segmented. However, extraction results could
become unpredictable when the data are noisy or when
structures cannot be segmented well, as is often the case
with some MR images. Following the approach used to
solve similar problems in 2D images using deformable
contours
[46]
, elastic surface approaches were proposed
to solve the problem in 3D data. These surfaces are
sometimes called balloons, for their expanding proper-
ties, or shrink-wrapping surfaces with elastic properties,
or, in general, deformable surfaces. Like snakes, these
techniques usually tend to be computationally intensive
because of their iterative steps.
Surface visualization
Although presenting a 3D-volume image is a fairly com-
plex problem, there are other ways of displaying or
extracting geometrical information that have been well
accepted for certain applications. The approach, which is
similar to isocontour lines in topographic data, extends
this concept to create a 3D surface to characterize 3D
image data. The technique came to be known as isosurface
extraction and was proposed by Marc Levoy and Bill
Lorensen
[19]
. The method works very successfully for
CT volume image data where the high signal-to-noise ratio
allows effective classification of constituent structures.
''Statistical'' surfaces
Recent approaches that attempt to produce efficient re-
sults for noisy data are ''statistical'' surfaces that employ
space partitioning techniques based on local statistical
measures to produce a mean estimated surface within
a given error deviation. This technique may not preserve
the topology connectivity that deformable techniques
could provide.
Isosurface extraction (''marching cubes'')
Volumetric images consist of a stack of 2D images and
can be considered as a 3D matrix of image data points.
The smallest fragment of the image is called a
voxel,
in
analogy to the concept of pixel in a 2D image. The sur-
face is extracted using a thresholding algorithm for each
cube of the lattice, marching through the entire volume.
In each cube, each pair of connected corners is examined
for a threshold-crossover point based on linear in-
terpolation. These points along each of the edges are
linked to form the isosurface on each cube, and the
process is repeated for the rest of the volume. Special
interpretation is required to handle cases that correspond
to multiple surfaces within the cube. The surfaces are
usually represented with triangles.
The advantage of this method is its fairly detailed
surface representation for objects of interest, as long as
the objects are easily separable in the data. However,
its computational load is high, and each time a new
threshold value is selected the generation of the new
surface may cause delays. The number of triangles pro-
duced by the method in a typical set of volume image
data is very large, typically on the order of tens of
thousands. Thus, displaying them all can be an intensive
graphic task. Adaptive surface extraction techniques
were later developed to address this problem using an
approach that coalesces coplanar triangles to be repre-
sented by a larger polygon. This can improve per-
formance substantially, as the number of vertices that
need to be processed in the transformation pipeline is
Wavelet surfaces
As discussed earlier, one of the problems of surface
representation is the number of triangles used to repre-
sent the surface. Recently, wavelet techniques, which
have inherently a multiresolution approach, have been
applied to describe surfaces. One major advantage of this
approach is that one can decide the desired resolution at
display time; thus, during periods of interaction a low-
resolution surface could be displayed, and when the in-
teraction ceases the higher resolution display of the
surface can be generated.
Volume visualization
The inherent limitation of the surface extraction method
is that it represents a specific threshold value in the data
and becomes restrictive or selective. Also, occasionally,
false surface fragments may be produced because of the
interpolation involved. Volumetric visualization methods
overcome these limitations and could help visualize as
much information as possible from the 3D volume image,
without being restrictive. This chapter presents only
a brief survey of issues in volume visualization.
