Biomedical Engineering Reference
In-Depth Information
(Fig. 7.13(d)) defined by the equation:
∂
I
∂
t
=
div
∇
I
1
+
[
∇
I
/
K
]
2
,
(7.45)
where the threshold
K
can be determined by a histogram of the gradient mag-
nitude. It was set to
K
=
300 in this example. The number of interactions of the
numerical scheme used [52] to solve this equation was 4.
Figures 7.13( b) and (e) show the cross section corresponding to the slice 40.
We observe that with anisotropic diffusion (Fig. 7.13(e)), the result is closer to
the boundary than with the Gaussian one (Fig. 7.13( b)).
Also, the final result is more precise when preprocessing with anisotropic
diffusion (Fig. 7.13(f )). This is expected because, according to Section 7.8,
Eq. (7.45) enables the blurring of small discontinuities (gradient magnitude be-
low
K
) as well as enhancement of edges (gradient magnitude above
K
).
Another point becomes clear in this example: The topological abilities
of T-surfaces enable the correction of the defects observed in the surface
extracted through steps (1)-(4). We observed that, after few interactions,
the method gives two closed components. Thus, the reconstruction becomes
better.
The T-surface parameters used are:
c
=
0
.
65,
k
=
1
.
32, and
γ
=
0
.
01. The grid
resolution is 5
×
5
×
5, freezing point is set to 15, and threshold
T
∈
(120
,
134)
in Eq. (7.12). The number of deformation steps for T-surfaces was 17. The model
evolution can be visualized in http://virtual01.lncc.br/ rodrigo/tese/elipse.html.
7.9.2 Artery Reconstruction
This section demonstrates the advantages of applying T-surfaces plus isosurface
methods. Firstly, we segment an artery from an 80
×
86
×
72 image volume ob-
tained from the Visible Human project. This is an interesting example because
the intensity pattern inside the artery is not homogeneous.
Figure 7.14(a) shows the result of steps (1)-(4) when using
T
∈
(28
,
32) to
define the object characteristic function (Eq. (7.27)). The extracted topology
is too different from that of the target. However, when applying T-surfaces the
obtained geometry is improved.
Figure 7.14( b) shows the result after the first step of evolution. The
merges among components improve the result. After four interactions of the
