Biomedical Engineering Reference
In-Depth Information
1.0
0.8
0.6
0.4
0.2
1 Unit Dilation, Discrete
1 Unit Dilation, Continuous
0.0
1
10
100
Sphere Radius
Figure 11.12:
Dependence of SI values on size for spherical objects. The squares
show SI values computed from discrete numerical simulation of dilation by one
voxel. The solid line shows SI values for the continuous case (Eq. 11.9). Note
that while the units on the horizontal axis are voxels for the discrete case, they
are arbitrary units for the continuous case.
et al.
[16] reported mean SI values of 0
.
96 for segmentation of the human brain
from MR images and mean SI values of only 0
.
85 for segmentation of smaller
brain structures such as the caudate.
In Fig. 11.13, the average volumes of the anatomical structures in the bee
brain images under consideration are shown with the actual segmentation
accuracies achieved for them using one of the segmentation methods discussed
later (MUL). It is easy to see that the larger a structure, the more accurately it
was typically segmented by the atlas-based segmentation. This confirms the the-
oretical treatment above and illustrates the varying bias of the SI metric when
segmenting structures of different sizes.
11.5.3
Bias from Structure Shape
A simple numerical measure that characterizes the shape of a geometrical object
is its surface-to-volume ratio (SVR). For a discrete set of labeled voxels in a
segmented structure, we can approximate the SVR
ρ
as the ratio of the number
of surface voxels
N
s
to the total number of voxels
N
t
, that is,
N
s
N
t
ρ
≈
(11.10)
