Biomedical Engineering Reference
In-Depth Information
The segmentation can be completed by user interaction based on the following
steps: (a) define a cutting plane; (b) set to zero the grid nodes belonging to the
triangles that the plane cuts and that are interior to the T-Surface; (c) apply steps
(4)-(6) above. The grid nodes set to zero become burnt nodes. Thus, the entropy
condition will prevent intersections of the surfaces generated. Hence, they will
not merge again.
Figure 9d shows the final result. The T-Surface parameters are:
c
=0
.
65,
k
=1
.
32, and
γ
=0
.
01. The grid resolution is 5
×
5
×
5, the freezing point is set
to 15, and threshold
T
∈
(120
,
134) in Eq. (4).
6.3. Artery Segmentation
In this section we demonstrate the advantages of applying T-Surfaces plus
isosurface methods. First, we segment an artery from an 80
×
86
×
72 image
volume obtained from the Visible Human project. This in an interesting example
because the intensity pattern inside the artery is not homogeneous.
Figure 10a shows the result of steps (1)-(4) when using
T
∈
(28
,
32) to define
the object characteristic function (Eq. (7)). The extracted topology is too different
from that of the target. However, when applying T-Surfaces the obtained geometry
is improved.
Figure 10b shows the result after the first step of evolution. The merges among
components improve the result. After 4 iterations of the T-Surfaces algorithm, the
extracted geometry becomes closer to that of the target (Figure 10c).
However, the topology remains different. The problem in this case is that
the used grid resolution is too coarse if compared with the separation between
branches of the structure. Thus, the flexibility of the model was not enough to
correctly perform the surface reconstruction.
The solution is to increase the resolution and take the partial result of
Figure 10c to initialize the model at the finer resolution. In this case, the cor-
rect result is obtained only with the finest grid (1
×
1
×
1). Figure 10d shows
the desired result obtained after 9 iterations. We also observe that new portions
of the branches were reconstructed due to increasing the flexibility of T-Surfaces
obtained through the finer grid. We should emphasize that an advantage of the
multiresolution approach is that at the lower resolution, small background artifacts
become less significant relative to the object(s) of interest. Besides, it avoids the
computational cost of using a finer grid resolution to get closer to the target (see
Section 2.2).
The T-Surfaces parameters are
γ
=0
.
01,
k
=1
.
222, and
c
=0
.
750. The
total number of evolutions is 13. The number of triangular elements is 10104 for
the highest resolution, and the CPU time was on the order of 3 minutes.
Sometimes, even the finest resolution may not be enough to get the correct
result. Figure 11a depicts such an example.
