Image Processing of Diffusion Tensor MRI Data - Advance Image Processing in Magnetic Resonance Imaging - page 430

(a)

(b)

FIGURE 13.8 (a) Diffusion tensors, weighted with their linear measure c l , from an axial slice
of a human brain. (b) Averaged diffusion tensors using a 5 × 5 × 3 Gaussian kernel weighted
with their linear measure c l , resulting in a macrostructural measure of fiber tract organization.
(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.)

As mentioned in the preceding text, in three dimensions, a diffusion tensor can
be visualized as using an ellipsoid in which the principal axes correspond to the
tensor's eigenvector system. However, it is difficult to distinguish between an edge-
on, flat ellipsoid and an oblong one using the surface-shading information. Similar
ambiguity exists between a face-on, flat ellipsoid and a sphere. We propose a tech-
nique for the visualization of tensor fields that overcomes the problems with ellip-
soids. Figure 13.9 compares the ellipsoidal representation of a tensor (left) with a
composite shape of linear, planar, and spherical components (right). The components

FIGURE 13.9 Comparison of an ellipsoid and a composite shape depicting the same
tensor with eigenvalues λ 1 = 1, λ 2 = 0.7, and λ 3 = 0.4 [24].