Biomedical Engineering Reference
In-Depth Information
Constraining the cortical thickness during the segmentation process prevent the
collapse of leakage of the surfaces.
The level set segmentation method with surface coupling is described in the
first section of this chapter. The traditional gradient features in the speed term
were replaced with tissue interface probability measurements based on statisti-
cal priors summarized here. The statistical models are based on the assumption
of Gaussian independent distribution functions of voxel intensities in MRI vol-
ume data for WM, GM, and CSF. Let us assume the presence of two tissue types
A
and
B
in the data with independent Gaussian probabilities
G
(
µ
A
,σ
A
) and
G
(
µ
B
,σ
B
). For each voxel
s
, a set of 26 immediate 3D-neighborhood voxels can
be defined. For each neighbor voxel, a normal direction
θ
along the line passing
through the center voxel and the neighbor voxel is computed which defines a
plane that separates the neighborhood into two regions (
R
1
,
R
2
). The probabil-
ity of the center voxel belonging to an interface between the two tissue types
(
A
,
B
)
is then computed as:
−
(
I
(
r
)
−
µ
A
)
2
σ
1
√
2
πσ
A
exp
p
AB
(
θ
)
=
r
∈
R
1
2
A
(2.42)
−
(
I
(
r
)
−
µ
B
)
2
σ
1
√
2
πσ
B
exp
×
r
∈
R
2
B
where
I
(
r
) is the intensity value of the data at neighbor voxel
r
. The final den-
sity probability at voxel
s
is set to the highest value of
p
AB
(
θ
) over all the 26
directions. An illustration of a feature map based on this tissue interface prob-
ability measure is provided on a single brain MRI slice computed with
(
R
1
,
R
2
)
containing only one voxel. The example illustrates well the better performance
of the interface probability feature at extracting locations of tissue transitions
for WM, GM, and CSF when compared to standard gradient maps.
Experiments:
Validation was performed on T1-weighted MRIs. The seg-
mentation process was initialized with several pairs of concentric spheres with
a constraint on starting inside the WM for robust behavior.
1.
The first experiment used simulated MRI data from the McConnell Brain
Imaging Center at the Montreal Neurological Institute [93]. The authors simu-
lated T1-weighted brain MRIs with 3% noise and 1 mm
3
voxel size. The distance
range between two surfaces was set to [1.5 mm 5.5 mm] leading to bandwidth
ranges for the inner and outer surfaces of [
−
3 mm 6 mm] and [
−
6 mm 3 mm],
respectively. Segmentation was validated by comparing the binary segmented
