Biomedical Engineering Reference
In-Depth Information
content especially where stained pathology specimens are concerned. In order
to apply the GVF deformable model strategy to chromatic pathology images, a
robust color GVF deformable model [17] based on
Luv
color gradients and
L
2
E
robust estimation was proposed for segmenting stained blood smear specimens.
Geometric deformable models, or level set-based deformable models, were almost
simultaneously proposed by Caselles et al. [6] and by Malladi et al. [5] to ad-
dress the fact that parametric active contour models could not resolve topological
changes. Geodesic deformable models are based on the theory of curve evolution
and are numerically implemented using level set methods. They can automati-
cally handle topology changes in an image and allow for multiple simultaneous
boundary estimations. Furthermore, they are not sensitive to initial starting posi-
tions as parametric deformable models are. Therefore, these groups of deformable
models continue to gain increasing interests throughout the research community
[18, 19, 20, 21]. However, due to their computational complexity, their speed of
convergence is slower than parametric deformable models. In addition, because of
the inaccuracy in the computation of the level set, this group of deformable mod-
els may sometimes need to be reinitialized several times throughout the whole
iterative procedure.
1.1. A Quick Look at Deformable Model
Defined within an image domain, the traditional deformable model [4] is
parametrically defined as
x
(
s
)=(
x
(
s
)
,y
(
s
)), where
x
(
s
) and
y
(
s
) are
x
and
y
coordinates along the contour and
s
represents the arc-length with value in [0
,
1],
to minimize an energy function as follows:
1
E
df
=
(
E
int
(
x
(
s
)) +
E
ext
(
x
(
s
)))
ds,
(1)
0
where the first term represents the internal energy of deformable model, and the
second term represents the external forces pushing the deformable model toward
the desired objects' edges. The internal energy is defined as
|
x
s
(
s
)
|
2
+
β
|
x
ss
(
s
)
|
2
)
/
2
,
E
int
(
x
(
s
))=(
α
(2)
where
x
ss
(
s
) is the second derivative of
x
(
s
) with respect to
s
. The external energy is defined as the image energy, which
is derived from the image data over the position that the deformable model lies.
This energy function attracts deformable models to salient features in images such
as lines and edges. The edges of the image is actually the boundary between color
differences. Therefore, the external energy is usually defined as follows:
x
s
(
s
) is the first derivative of
x
(
s
) and
∇
G
σ
(
x,y
)
∗
I
(
x, y
)
,
E
ext
(
x
(
s
)) =
−
(3)