Biomedical Engineering Reference
In-Depth Information
that it is easy to compute and gives preferences to certain corners (see [89]):
λ
RGB
+
∇
Φ=
+
λ
RGB
,
(22)
−
where
2
2
2
,
2
2
2
∂R
∂x
∂G
∂x
∂B
∂x
∂R
∂y
∂G
∂y
∂B
∂y
g
11
=
+
+
22
=
+
+
and
∂R
∂x
·
∂R
∂y
+
∂G
∂x
·
∂G
∂y
+
∂B
∂x
·
∂B
∂y
.
g
12
=
g
21
=
3.2.2. Color GVF snake
Once we achieve the edge map of the color image using Eq. (22), the extension
of the graylevel GVF snake to its color counterpart is straightforward. Substituting
Θ
color
for the original GVF vector field Θ in Eq. (7), we have
x
(
s
)
−
x
(
s
)+Θ
color
=0
,
α
β
(23)
where Θ
color
is the color gradient vector flow, defined as Θ
color
=(
u
color
(
x, y
),
v
color
(
x, y
)) that minimizes the following energy function:
µ
u
x
+
u
y
+
v
x
+
v
y
+
|∇
Φ
|
2
·|
Θ
color
−∇
Φ
|
2
dxdy,
ε
=
(24)
∇
Φ is given in (22).
The rest of the numerical implementation of color the GVF snake is similar to
that for the graylevel GVF snake. The solution of
u
color
and
v
color
can be derived
from the iterative algorithm for (9), and the snake curve will move forward to the
vicinity of the object boundary.
It is worth mentioning that in (3) larger
σ
values will cause the boundaries to
become blurry if a Gaussian smoothing operation is adopted. Such large
σ
values
are often necessary, however, in order to increase the capture range of the snake.
To address this problem, we replaced it with the anisotropic diffusion technique
proposed by Sapiro and Ringach [90]. A comparison of these two techniques can
be seen in Figure 3, which gives an example of finding the contour of a seed using
the proposed color GVF snake.
In Figure 3 we also show the convergence results with different initial curves:
one inside the seed (Figure 3e) and the other outside the seed (Figure 3f ). Both
can arrive at the correct boundary of the seed, which represents the property of
initialization insensitivity derived from the graylevel GVF snake. Finally, we
compare the closeups of two external force fields in the color GVF snake and a
classical snake. It is obvious that, while the external forces of the classical snake
are rather disordered, those of the color GVF snake correctly point toward the seed
boundary.
where
