Biomedical Engineering Reference
In-Depth Information
Figure 3.
The image segmentation result of a Follicular Center Cell Lymphoma (FCC)
applying the GVF 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.
∇
G
σ
(
x,y
)
∗
f
(
x, y
)
is the gradient of the input image
f
(
x, y
)
where
after
Gaussian smoothing with variance
σ
and mean
0
. Equation (25) is dominated
when
∇
G
σ
(
x,y
)
∗
f
(
x, y
)
by
u
x
u
y
v
x
v
y
+
+
+
is small. When
∇
G
σ
(
x,y
)
∗
f
(
x, y
)
is large, the second term dominates the integrand and
is minimized when Θ=
∇
G
σ
(
x,y
)
∗
f
(
x, y
)
. This result keeps Θ nearly equal
to the gradient of the edge when the deformable model is near the object, while
enabling the deformable model to move toward the edges when it is far away from
the object.
Figure 3 shows the performance using the GVF deformable model for seg-
menting a Follicular Center Cell Lymphoma (FCC). Based on the results of these
experiments, we have demonstrated that the GVF deformable model provides large
capture regions and at the same time the GVF vector flow enables the deformable
model to enter into convex regions within the image. In fact, the GVF deformable
model outperformed all the other gradient-based single-channel image segmenta-
tion algorithms that were tested. (Please note that all segmentation results were
obtained after applying the color gradients in [17]; using the traditional gradient
[15] does not result in accurate delineation of the boundaries.
3.4. Robust Color GVF Deformable Model
In graylevel images, the gradient is defined as the first derivative of the image
luminance. It has a high value in those regions exhibiting high luminance contrast.
However, this strategy is not suitable for color images. Simply transforming color
images into graylevel images by averaging across the three channels and applying
the graylevel image gradient operator does not provide satisfactory results for many
pathology applications.
Imaged pathology specimensmust be accurately segmented before any higher-
level analysis can be performed. In order to apply the GVF deformable model to
