Biomedical Engineering Reference
In-Depth Information
4.2. Geodesic Active Contour Models
The geodesic model was proposed in 1997 by Caselles et al. [54]. This
involves a problem of geodesic computation in a Riemannian space, according
to a metric induced by the image. Solving the minimization problem consists in
finding the path of minimal new length in that metric:
1
C
(
s
)
|
J
(
C
)=2
|
.g
(
|∇
u
0
(
C
(
s
))
|
)
ds,
(14)
0
where the minimizer
C
will be obtained when
g
(
|∇
u
0
(
C
(
s
))
|
) vanishes, i.e., when
the curve is on the boundary of the object. The geodesic active contour model also
has a level set formulation as follows:
∂
∂t
=
|∇
Φ
|
(
div
(
g
(
|∇
u
0
|
)
∇
Φ
|∇
Φ
|
)+
νg
(
|∇
u
0
|
))
.
(15)
The geodesic active contour model is based on the relation between active
contours and the computation of geodesics or minimal distance curves. The mini-
mal distance curve lies within a Riemannian space whose metric is defined by the
image content. This geodesic approach for object segmentation allows connecting
classical “snakes” based on energy minimization and geometric active contours
based on the theory of curve evolution. Previous models of geometric active con-
tours are improved, allowing stable boundary detection when their gradients suffer
from large variations.
4.3. Tuning Geometric Active Contour with Regularizers
The main problem of boundary-based level set segmentation methods is re-
lated to contour leakage at locations of weak or missing boundary data information.
One approach can be followed to solve these limitations: to fuse regularizer terms
in the speed function.
Suri et al. review in [1] recent works on the fusion of classical geometric and
geodesic deformable models speed terms with regularizers, i.e., regional statistics
information from the image. Regularization of the level set speed term is desirable
to add prior information on the object to segment and prevent segmentation errors
when using only gradient-based information in definition of the speed. Four main
kinds of regularizers were identified by the review authors:
1. clustering-based regularizers;
2. Bayesian-based regularizers;
3. Shape-based regularizers;
4. Coupling-surfaces regularizers.
We will now give a brief overview of each method.
