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thickness. For sake of comparison, VBs are segmented using other alternatives: the
graph cuts [
36
] without shape constrained (
A
1
), statistical level sets (
A
2
) method
[
41
], and the b-spline based interpolation (
A
3
).
Evaluation
We calculate the percentage segmentation error from the ground truth in order to
evaluate the segmentation results as follows:
S
a
\
S
m
e%
¼
100
ð
1
S
m
Þ
ð
42
Þ
S
a
[
where S
m
and S
a
represent manually and automatically segmented VBs,
respectively.
The statistical analysis of our method is shown in the Table
6
. In this table the
results of the proposed segmentation method and other three alternatives are shown.
The average error of the VB segmentation on 30 clinical data sets is 6.8 % for the
proposed method. Notice that it is dif
cult to separate the VB and spine processes
because they have very similar gray level information. However, our shape model
successfully extracts the spine processes. While other alternative methods fail to
completely separate the processes and so they have huge precision error, which may
change the BMD measurements. Figure
36
shows an example of 3D segmentation
results of all tested methods for a clinical data set. The misclassi
ed voxels, in this
figure, are represented by red color.
Validation
ESP, which was scanned at 120 kVp and 0
75 mm slice thickness, is accepted as a
standard for quality control in bone densitometry [
3
]. Therefore, we segment ESP in
order to evaluate the proposed segmentation algorithm. The proposed approach
accurately segments the VB without its processes and with a segmentation error
2.6 % as shown in Fig.
37
.
:
Table 6 Accuracy and time
performance of our VB
segmentation on 30 data sets
Algorithm
Error %
Our
A
1
A
2
A
3
Min. error, %
1.5
5.7
6.5
15.2
Max. error, %
17.3
83.2
91.2
97.7
Mean error, %
6.8
37.8
43.1
51.6
Stand. dev.,%
4.3
28.6
31.1
33.4
Average time, seconds
9.1
8.3
41.5
8.9
