Biomedical Engineering Reference
In-Depth Information
would like to draw your attention to the fact that a change in the geometry of each
case (represented by the changes in structure of the gyrifications between normal
and dyslexic, and changes between individuals as well) is expected to affect the
volumetric measurements. Figure 9 illustrates the change in geometry. Thus,
the basic goal of fixing the depth is to be able to study fairly the effect of these
geometric changes (using the volume as a quantitative parameter) that is directly
related to the number and width of minicolumns.
Figure 9.
The difference in geometry between normal and dyslexic brains. The marked
areas show that the gyrifications in the normal brain (right image) is much more complex
than its corresponding part in the dyslexic brain.
The parcellation algorithmwas designed and tested on both synthetic and MR
images. The basic idea of the algorithm is to calculate the sign distance function
φ
from the boundary Γ (the outer contour of the white matter). This function has
the following properties [45]:
d
(
x
),if
x
inside of
W
(white matter point)
,
0,if
x
φ
(
x
)=
∈
Γ
,
(18)
−
d
(
x
),if
x
outside of
W,
where
d
(
x
) = min
y∈
Γ
(
|
x
−
y
|
)
,
and
W
: the region enclosed by Γ
.
(19)
The boundary between the inner and outer compartments is obtained by detecting
the set
X
=
{
of all points that are
d
1
away from the boundary Γ,
that is, the set
X
represents a contour that is distant from the outer contour by
d
1
pixels. Figure 10 illustrates this idea, which simply consists of representing the
outer contour as the zero level set that is the intersection of the plane
z
=0(the
blue plane) with the signed distance function. Pushing the contour inward is done
by getting the intersection of the plane
z
=
d
1
x/d
(
x
)=
d
1
}
(the green plane) with the signed
distance function.
Figure 11 shows the result of applying the algorithm on a synthetic image of
a circle, whereas Figure 12 shows the parcellation results on a real MRI slice.
After parcellating the white matter and isolating the outer compartment, the
volumes of the whole white matter (
V
) as well as the volume of the outer com-
