Biomedical Engineering Reference
In-Depth Information
(a)
(b)
Figure 11.
Using the front-evolving geometric model for segmentation of living tumor
cells in the LSDCAS system: (a) original image; (b) result. See attached CD for color
version.
where Φ is the level set function corresponding to the current curve
C
,
g
() is the
gradient function on the image, and
γ
is a constant to regulate the evolving speed.
The following is an example using the front-moving geometric model for
image segmentation in a living tumor cell analyzed using the LSDCAS system
[50]. The result is shown in Figure 11. The border of the image was chosen as the
initial location of the contour, and the moving direction was initialized as inward.
The special property of the microscopic image is that at some points of the
cell boundary the contrast is very low and the gradient from the original image data
is not strong enough for accurate segmentation. In order to solve this problem, a
preprocessing is applied for image boundary enhancement to prevent the moving
front fromevolving into the internal portion of the cells, which haveweak boundary
areas. The method is adopted from [20]. The original method is for color images
with multiple bands, but the microscopic imaging here is gray-valued. So, let
θ
(
x, y
):
R
2
→
R
, and the arc is defined as
∂θ
∂x
dx
+
∂θ
∂y
dy.
dθ
=
(9)
The norm is defined as:
∂θ
2
∂x
2
∂θ
2
∂y
2
∂θ
2
∂x∂y
dxdy.
dθ
2
=
dxdx
+
dydy
+2
(10)
dx
dy
T
s
xx
dx
dy
,
s
xy
dθ
2
=
(11)
s
xy
s
yy
∂θ
∂θ
∂θ
∂θ
where the second-order derivatives
s
xx
=(
∂x
)
.
(
∂x
),
s
yy
=(
∂y
)
.
(
∂y
),
s
xy
=
∂θ
∂x
)
.
(
∂θ
∂y
).
s
yx
=(
