Biomedical Engineering Reference
In-Depth Information
where max
{
χ
1
,χ
2
}
=1. Observe that they are enclosed by a merger of the
contours. This merge can be approximated by a curve belonging to the region
obtained by tracing the transverse triangles. The same would be true for more than
two contours (and, obviously, for only one).
After the reparameterization process, a suitable evolution scheme must be
applied, as described in the following section.
Figure 2.
Two snakes colliding with the inside grid nodes and snaxels marked.
2.1.1. Discrete Model
A T-Surface can be seen as a discrete form of the parametric deformable
surfaces given by Eq. (1) [10]. It is defined as a closed elastic mesh. Each node
is called a
node element
, and each pair of connected nodes
v
i
,v
j
is called a
model
element
.
The node elements are linked by springs, whose natural length we set to zero.
Hence, a tensile force can be defined by:
α
i
=
j
S
ij
where
S
ij
=
c
(
r
ij
)
,
(3)
where
c
is a scale factor and
r
ij
is the length of the corresponding
model element. The model also has a normal force that can be weighted as follows
[10]:
=
v
i
−
v
j
F
i
=
k
(
sign
i
)
n
i
,
(4)
where
n
i
is the normal vector at node
i
,
k
is a scale factor, and sign
i
=+1if
I
(
v
i
)
>T
and sign
i
=
−
1 otherwise (
T
is a threshold of the image
I
). This
force is used to push the model toward image edges until it is opposed by external
image forces.
