Biomedical Engineering Reference
In-Depth Information
Figure 2.
The image segmentation result of a Follicular Center Cell Lymphoma (FCC)
applying the balloon deformable model. The left panel shows the initial position, the center
panel shows one snapshot of the evolving contours, and the right panel shows the final
segmentation results after 150 iterations. See attached CD for color version.
point; we have
P
(
x
)=
g
(
d
(
x
)), and there are many ways to define the function
P
. For example,
e
−d
(
x
)
2
.
P
=
−
(23)
Figure 2 shows the performance of applying the traditional deformable model
on segmenting a Follicular Center Cell Lymphoma (FCC). Although it provides
better performance compared to the traditional deformable model, it still fails to
segment nuclei accurately. (Notice that all the segmentation results are obtained
after applying the color gradients in [17]; otherwise, the result will not converge
to the nuclei if applying the normal gradient used in [13].)
3.3. GVF Deformable Model
To effectively capture concave regions in graylevel images and enlarge the
capture region of the traditional deformable model, Xu and Prince [15] proposed
a new force field into the external force. The Helmholtz theorem [24] states that
the most general static vector field can be decomposed into two components: an
irrotational (curl-free) component and a solenoidal (divergence-free) component.
The traditional force field is a static irrotational vector field. The GVF deformable
model generates a more general field by combining these two components.
Rewriting (5) and replacing
−∇
E
ext
(
x
(
s
)) with Θ,
x
t
(
s, t
)=
α
x
ss
(
s, t
)
−
β
x
ssss
(
s, t
)+Θ
,
(24)
where Θ is the gradient vector flow defined as Θ(
x, y
)=[
u
(
x, y
)
,v
(
x, y
)], that
minimizes the energy functional
µ
(
u
x
+
u
y
+
v
x
+
v
y
)
dx dy
+(
∇
G
σ
(
x,y
)
∗
Ψ=
f
(
x, y
)
2
·
Θ
−∇
G
σ
(
x,y
)
∗
f
(
x, y
)
2
)
dx dy,
(25)
