Image Processing Reference
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(a)
(b)
FIGURE 13.7 A 2-D diffusion tensor field (a) and the effect of relaxation using a Gaussian
filter (b). Note how the tensors in an inconsistent region become rounder, whereas in
consistent areas their orientation is stabilized. (From Westin, C.-F., Maier, S., Mamata,
H., Nabavi, A., Jolesz, F., and Kikinis, R. (2002). Processing and visualization of diffusion
tensor MRI. Med. Image Anal. 6(2): 93-108.)
13.4
VISUALIZATION OF DIFFUSION TENSORS
Several methods have been proposed for visualizing the information contained
in DT-MRI data. Pierpaoli et al. [17] render ellipsoids to visualize diffusion data
in a slice. Peled et al. [15] used headless arrows to represent the in-plane com-
ponent of the principal eigenvector, along with a color-coded out-of-plane com-
ponent. Recently, Kindlmann and Weinstein [10] applied our geometric shape
indices [25] to opacity maps in volume rendering. They termed this method
barycentric opacity mapping . They compare volume renderings using opacity
maps based on the indices c l , c p , and c a (Equation 13.15-Equation 13.18).
In Figure 13.8a , a diffusion tensor field from an axial slice of the brain is
shown (using the visualization method presented in Reference 15) and the filtered
tensor field (Figure 13.8b). Prior to visualization, the tensors were weighted with
their linear diffusion measures.
The filtered images show the result of applying the macrostructural measure
presented in Subsection 13.3.2. First a 5
3 Gaussian window, a , with
standard deviation 2 mm was applied to the data (Equation 13.25). Because the
out-of-plane resolution is slightly less than half the in-plane resolution, there is
almost no smoothing performed between the slices. The tensors resulting from
the Gaussian filtering D a (Equation 13.25) have been weighted with their linear
diffusion measures, c l (Equation 13.15), respectively. The result illustrates the
fact that the filtering increases the rank of the tensors in nonstructured areas
because the linear measures are decreased in those areas.
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