Biomedical Engineering Reference
In-Depth Information
∂
∂t
=
s
(
x
)
stopping force
c
1
2
δ
1
(Φ)
c
2
2
(
δ
1
(Φ) (1
c
3
2
δ
2
(Φ)
λ
1
I
0
|
−
|
−
λ
2
I
0
|
−
|
−
H
2
(Φ))
−
H
1
(Φ)
δ
2
(Φ))
−
λ
3
I
0
|
−
|
,
region force
(32)
where
s
(
x
) is defined as
1
s
(
x
)=
.
H
(
P
(
x
))
|
2
1+
|
The terms within the curly braces describe the propagating force from the com-
petition of three regions. The
s
(
x
) term beyond the curly braces is the stopping
term that decreases to zero at coupled boundaries;
H
(
·
) is defined heuristically
according to the experimental data. Fortunately, a specific form of
H
(
·
) that is
appropriate for most MR brain data is found and given in the experimental section.
Thus, this formulation borrows the strength of robustness from the region forces,
and simultaneously incorporates the accurate localization ability of the coupled
boundary detector.
5.2.4. GM/CSF segmentation
After obtaining the WM/GM surface as described in the previous subsection,
we move on to GM/CSF segmentation, where the WM/GM surface is fed as input.
GM/CSF segmentation is close to WM/GM segmentation except in one aspect. In
GM/CSF segmentation, we replace the coupled edge detector with a conventional
single edge detector because only the GM/CSF surface, and not two surfaces, is
outside the evolving surface. Thus, we formulate our PDE for GM/CSF segmen-
tation as follows:
c
3
)
2
δ
(Φ)
,
∂
∂t
=
H
1
(Φ)
·
c
2
)
2
+
λ
3
(
I
s
(
x
)
·
−
λ
2
(
I
−
−
(33)
1
where
s
(
x
)=
1+
|∇I
(
x
)
|
2
, and all other notations are the same as in the previous
subsection.
The right-hand side of Eq. (33) is a propagation term propelled by regional
force, but also confined by the boundary detector. The surface is initiated at the
WM/GM surface and evolves into the GM until it reaches the GM/CSF surface.
