Biomedical Engineering Reference
In-Depth Information
4.3.1. Clustering-Based Regularizers
Clustering-based regularizers
: Suri [31] has proposed the following energy
functional for level set segmentation:
∂
∂t
=(
εk
+
F
p
)
|∇
Φ
|−
F
ext
∇
Φ
,
(16)
where
F
p
is a regional force term expressed as a combination of the inside and
outside regional area of the propagating curve. The term is proportional to a
region indicator taking a value between 0 and 1, derived from a fuzzy membership
measure. The second part of the classical energy model constituted the external
force given by
F
ext
. This external energy term depends upon image forces that
are a function of the image gradient.
4.3.2. Bayesian-based regularizers
Baillard et al. [35] proposed an approach similar to the previous one where
the level set energy functional is expressed as
∂
∂t
=
g
(
|∇
|
)(
k
+
F
0
)
|∇
Φ
|
I
.
(17)
It employs a modified propagation term
F
0
as a local force term. This term was
derived from the probability density functions inside and outside the structure to
be segmented.
4.3.3. Shape-based regularizers
Another application of the fusion of Bayesian statistics with the geometric
boundary/surface to model the shape within the level set framework was done
by Leventon et al. [36]. The authors introduced shape-based regularizers where
curvature profiles act as boundary regularization terms more specific to the shape
in order to extract more than standard curvature terms. A shape model is built
from a set of segmented exemplars using principal component analysis applied to
the signed-distance level set functions derived from the training shapes (analogous
to Cootes et al.'s [55] technique). The principal modes of variation around a mean
shape are computed. Projection coefficients of a shape on the identified principal
vectors are referred to as shape parameters. Rigid transformation parameters
aligning the evolving curve and the shape model are referred to as pose parameters.
To be able to include a global shape constraint in the level set speed term, shape
and pose parameters of the final curve Φ
∗
(
t
) are estimated using the maximum a
posteriori estimation. The new functional is the solution for the evolving surface,
expressed as
∇
Φ)+
λ
2
(Φ
∗
(
t
)
−
Φ(
t
))
,
(18)
Φ(
t
+1)=Φ(
t
)+
λ
1
(
g
(
|∇
I
|
)(
k
+
c
)
|∇
Φ
|
+
∇
g
(
|∇
I
|
)
.
