Biomedical Engineering Reference
In-Depth Information
segment. The authors also modified the data consistency term
g
(
|∇
I
|
) as ex-
pressed in Eq. (2.9) using a transitional probability from going inside to outside
the object to be segmented.
(3)
Shape-based Regularizers
: Leventon
et al.
[31] introduced shape-based
regularizers where curvature profiles act as boundary regularization terms more
specific to the shape to extract than standard curvature terms. A shape model is
built from a set of segmented exemplars using principle component analysis ap-
plied to the signed-distance level set functions derived from the training shapes.
The principal modes of variation around a mean shape are computed. Projec-
tion 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 maximum
a posteriori
estimation.
The new functional is derived with a geodesic formulation as in Eq. (2.18) with
solution for the evolving surface expressed as:
φ
(
t
+
1)
=
φ
(
t
)
+
λ
1
(
g
(
|∇
I
|
)(
c
+
κ
)
|∇
φ
(
t
)
|+∇
g
(
|∇
I
|
)
.
∇
φ
(
t
))
(2.21)
+
λ
2
(
φ
∗
(
t
)
−
φ
(
t
))
,
where (
λ
1
,λ
2
) are two parameters that balance the influence of the gradient-
curvature term and the shape-model term. In more recent work, Leventon
et al.
[32] introduced further refinements of their method by introducing prior in-
tensity and curvature models using statistical image-surface relationships in
the regularizer terms. Limited clinical validation have been reported using this
method but some illustrations on various applications including segmentation
of the femur bone, the corpus callosum and vertebral bodies of the spine showed
efficient and robust performance of the method.
(4)
Coupling-surfaces Regularizers
: Segmentation of embedded organs
such as the cortical gray matter in the brain have motivated the introduction
of a level set segmentation framework to perform simultaneous segmentation
of the inner and outer organ surfaces with coupled level set functions. Such
method was proposed by Zeng
et al.
in [33]. In this framework, segmentation is
performed with the following system of equations:
φ
in
+
V
in
|∇
φ
in
| =
0
φ
out
+
V
out
|∇
φ
out
| =
0
(2.22)
