Biomedical Engineering Reference
In-Depth Information
normalization process, the positions of the control points in the unnormalized
image are determined. The affine transformation corresponding to these image
can then be determined by running a special search procedure.
7.4 Initialization of T-Surfaces
All the methods described in Section 7.3 suffer from a common limitation: Self-
intersections may happen during the evolution of the initial curve/surface.
Traditional deformable models [6, 19, 42], including the one defined by
Eq. (7.9), cannot efficiently deal with self-intersections. It is due to the non-
local testes dependency, which requires
O
(
N
2
) in the worst case, where
N
is
the number of mesh nodes (or snaxels, for 2D).
Recently, in [63] we have shown that such limitation can be addressed by
using the T-snakes model because the reparameterization process of this model
can naturally deal with self-intersections. It can also be addressed for 3D by
using the T-surfaces.
Firstly, let us make some considerations about the T-snakes/T-surfaces.
The threshold
T
used in the normal force definition (7.12) plays an important
role in the T-surfaces model [47, 49]. If not chosen properly, the T-surfaces can
be frozen in a region far from the target(s) [33, 63].
The choice of
T
is more critical when two objects to be segmented are too
close, as shown in Fig. 7.7. In this example, the marked grid nodes are those
whose image intensity falls bellow the threshold
T
.
For T-snakes model to accurately segment the pictured objects, it has to
burn the marked grid nodes. However, the normal force given by expression
(7.12) changes its signal if the T-snakes gets closer. So, the force parameters
Figure 7.7:
T-snake and grid nodes marked.
