Image Processing Reference
In-Depth Information
(a)
(b)
(c)
(a, b, and c) Coronal brain images showing the three geometrical measures.
Note that most of the major fiber tracts are visible despite the low resolution of the data
set (1.7
FIGURE 13.4
4 mm). (From Westin, C.-F., Maier, S., Mamata, H., Nabavi, A., Jolesz,
F., and Kikinis, R. (2002). Processing and visualization of diffusion tensor MRI.
×
1.7
×
Med.
Image Anal.
6(2): 93-108.)
Figure 13.4 contains coronal brain images depicting these geometrical mea-
sures. Alternatively, the coordinates can be normalized with the norm of the
tensor, giving:
λλ
λλλ
++
1
2
c l =
(13.15)
2
2
2
1
2
3
λλ
λλλ
2
(
++
)
2
3
c p =
(13.16)
2
2
2
1
2
3
λ
λλλ
3
3
c s =
(13.17)
2
++
2
2
1
2
3
To ensure that the measures remain in the range from 0 to 1, and the sum is 1,
the scaling factors 2 and 3 have been inserted for the planar and the spherical cases.
A geometrical anisotropy measure that has a behavior similar to the FA measure
(fractional anisotropy, Equation 13.6) describes the deviation from the spherical case
c
=− = +
1
c
c
c
(13.18)
a
s
l
p
 
Search WWH ::




Custom Search