Biomedical Engineering Reference
In-Depth Information
address the limitations of traditional approaches, Yang et al. [17] proposed a robust
color GVF deformable model that integrated a color gradient and robust estimation
in the original GVF deformable model. The definition of color gradients was first
introduced in [25, 26, 27]. In contrast to previous approaches, the color gradient
in [17] is defined in a
Luv
color space rather than an RGB color space because
Euclidean metrics and distances are perceptually uniform in a
Luv
color space,
which is not the case in an RGB color space [26].
Let Γ(
x, y
):
R
3
be a color image; based on classical Riemannian geometry
results [28], the
L
2
norm can be written in matrix form:
dx
dy
T
g
11
dx
dy
,
g
12
d
Γ
2
=
(26)
g
21
g
22
∂
∂y
]
2
. The quadratic form (26)
achieves its extrema changing rates in the directions of the eigenvectors of matrix
[
g
i,j
]
,i
=1
,
2
,j
=1
,
2 and the changing magnitude is decided by its eigenvalues
λ
+
and
λ
−
. Define the color gradient as
∇
Θ=
λ
+
−
∂
∂x
]
2
,g
12
=
g
21
=
∂
∂x
∂
∂y
,g
22
=[
where
g
11
=[
λ
−
,
(27)
where
2
∂x
2
∂L
∂y
∂L
∂x
2
2
∂u
∂u
∂y
g
11
=
g
22
=
,
(28)
∂x
2
∂v
2
∂v
∂y
∂
2
L
∂x∂y
∂
2
u
∂x∂y
g
12
=
g
21
=
,
(29)
∂
2
v
∂x∂y
where
L
,
u
, and
v
correspond to the three channels in the
Luv
color space. In
the robust color GVF deformable model, the initial contour locations are obtained
from
L
2
E
robust estimation [17] to increase the converge speed. By applying
the calculus of variations introduced in the previous section, it can be shown that
minimizing the integral in Eq. (25) is equal to solving the following equation:
∇
2
u
f
x
)(
f
x
+
f
y
)=
µ
−
(
u
−
,
(30)
∇
2
v
f
y
)(
f
x
+
f
y
)=
µ
−
(
v
−
.
(31)
