Biomedical Engineering Reference
In-Depth Information
(a)
(b)
(c)
(d)
Figure 21.
Circle segmented by the shape prior-based geodesic snake: (a) circle stained
by a bar and salt-and-pepper noise; (b) circle segmented by the geodesic snake; (c) prior
circle shape; (d) circle segmented by shape prior-based geodesic snake.
Then the speed field produced by the prior contour is
∇
ε
F
shape
(
X
)=
f
s
(
d
)
,
(44)
|∇
ε
|
where
F
shape
directs to the nearest shape point, and the magnitude of
F
shape
is
controlled by
f
s
.
The attributes of the prior shape force are very important. There are two kinds
of force: one like the elastic force that would be more powerful far away from
prior shape, and the other just like the force in an electric field, so that the closer to
the shape, the more powerful it will be. It is hoped that
F
shape
can only take effect
in the field nearby the prior contour and leave it alone far from the prior contour,
and the closer, the more powerful. So the second choice is taken. It is supposed
that the farthest neighborhood distance is
δ
:
k
(
δ
−
d
≤
δ,
d
)
f
s
(
d
)=
(45)
0
d>δ.
We then obtain the final shape prior-based geodesic snake equation:
∂φ
∂t
=
u
(
x
)(
k
+
v
0
)
|∇
ε
|∇
ε
|
·∇
∇
|
+
∇
·∇
φ
u
φ
+
f
s
(
d
)
φ.
(46)
The algorithm was demonstrated on a synthetic image. We found that we could
get a better result guided by a prior shape field (Figure 21). We set
δ
=15when
segmenting the circle.
6.4. Application and Results
We put the algorithm into practice and efficiently segmented heart valve
leaflets from 10 3D echocardiographic sequences, each covering a complete car-
diac cycle. The 3D sequences were recorded using a Philips Sonos 750 TTO probe,
