Biomedical Engineering Reference
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dataset ( V 2 ) is formed by calculating ( C 1 , C 2 , C 3 ) invariants for each voxel and
combining them into C a . It provides a measure of the magnitude of the anisotropy
within the volume. Higher values identify regions of greater spatial anisotropy
in the diffusion properties. A slice from the second scalar volume is presented
in Fig. 8.12 (right). The measure C a does not by definition distinguish between
linear and planar anisotropy. This is sufficient for our current study since the
brain does not contain measurable regions with planar diffusion anisotropy.
We therefore only need two scalar volumes in order to segment the DT
dataset.
We then utilize our level set framework to extract smoothed models from the
two derived scalar volumes. First the input data is filtered with a low-pass Gaus-
sian filter ( σ 0 . 5) to blur the data and thereby reduce noise. Next, the volume
voxels are classified for inclusion/exclusion in the initialization based on the
filtered values of the input data ( k 7 . 0 for V 1 and k 1 . 3 for V 2 ). For grayscale
images, such as those used in this chapter, the classification is equivalent to high
and low thresholding operations. The last initialization step consists of perform-
ing a set of topological (e.g. flood fill) operations in order to remove small pieces
or holes from objects. This is followed by a level set deformation that pulls the
surface toward local maxima of the gradient magnitude and smooths it with a
curvature-based motion. This moves the surface toward specific features in the
data, while minimizing the influence of noise in the data.
Figures 8.13 and 8.14 present two models that we extracted from DT-MRI
volume datasets using our techniques. Figure 8.13 contains segmentations from
volume V 1 , the measure of total diffusivity. The top image shows a Marching
Cubes isosurface using an isovalue of 7.5. In the bottom we have extracted just
the ventricles from V 1 . This is accomplished by creating an initial model with a
flood-fill operation inside the ventricle structure shown in the middle image. This
identified the connected voxels with value of 7.0 or greater. The initial model
was then refined and smoothed with a level set deformation, using a β value of
0.2.
Figure 8.14 again provides the comparison between direct isosurfacing and
and level set modeling, but on the volume V 2 . The image in the top-left corner is
a Marching Cubes isosurface using an isovalue of 1.3. There is significant high-
frequency noise and features in this dataset. The challenge here was to isolate
coherent regions of high anisotropic diffusion. We applied our segmentation
approach to the dataset and worked with neuroscientists from LA Childrens
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