Biomedical Engineering Reference
In-Depth Information
itself. But the whole valve moves within a relatively stationary region, which is
just in the ventricle. When it comes to a 3D echocardiographic sequence, the valve
can share the same region in different slices at the same time. So it can be in the
same sample position at different times. We can then segment several images under
the guidance of the same region. When the zero level set is limited to evolve in
the fixed region, the segmenting process will be more robust and efficient. We can
segment the whole 3D echocardiographic sequence based on several prior regions.
Consider a prior region Ω within which the valve moves. There is a region
function
J
(
x, y
):
1
(
x, y
)
∈
Ω
,
J
(
x, y
)=
(36)
0
(
x, y
)
/
∈
Ω
,
A speed field is created outside the prior region. The force of the field is zero
inside the prior region and direct to the prior region outside it. The power of the
force bears a close relation to the distance from the point to the prior region. So the
speed field has a potential to drive the zero level set to the prior region. In addition,
the prior force will obtain a balance with the inflating force nearby the boundary
of the region. When segmenting the valve, an appropriate contour can be obtained
at the root of the valve, lest the zero level set evolve to the whole cardiac wall. The
distance from point
X
to prior region Ω is defined as
d
(
X
)
∈
Ω
,
X/
γ
(
X
)=
(37)
0
X
∈
Ω
,
d
(
X
) = min (
|
X
−
X
I
|
)
X
I
∈
Ω
.
(38)
Then the speed field of the prior region is
γ
|∇
γ
|
∇
F
region
(
X
)=[
f
r
(
d
)+
c
1
]
,
(39)
where
c
1
is equal to or a little less than
v
0
;
f
r
(
·
) makes the prior force almost
c
1
nearby Ω and to rise to
c
1
+
c
2
far from Ω. We take
.
d
2
σ
2
f
r
(
d
)=
c
2
1
−
exp
−
(40)
A speed field is then obtained that can drive the zero level set to Ω.
The final region prior-based geodesic snake equation is
∂φ
∂t
=
u
(
x
)(
k
+
v
0
)
|∇
∇
γ
|
+
∇
·∇
|
·∇
φ
u
φ
+[
f
r
(
d
)+
c
1
]
φ.
(41)
|∇
γ
We can obtain a final result that includes the cardiac valve, the root of the valve,
and the raised cardiac wall that joggles with the valve with some postprocessing.
