Biomedical Engineering Reference
In-Depth Information
900
900
criterion
criterion
800
800
700
700
600
600
500
500
400
400
300
300
200
200
100
100
0
0
0
10
20
30
40
50
60
0
5
10
15
20
25
30
iteration number
time in seconds
5
5
warping index
warping index
4.5
4.5
4
4
3.5
3.5
3
3
2.5
2.5
2
2
1.5
1.5
1
1
0.5
0.5
0
0
0
10
20
30
40
50
60
0
5
10
15
20
25
30
iteration number
time in seconds
Figure 9.13: The evolution of the optimization process. The left column dis-
plays the evolution with respect to the number of iterations, while the right
column represents the same quantity respect to time. The first row shows the
SSD criterion
E
, the second row the warping index
. The steep (step) changes
correspond to the changes in the model and image resolutions. We observe good
correlation between all four graphs.
with the true deformation in Fig. 9.12, bottom-right. We note that the deformation
was well recovered with no perceptible difference.
The spatial distribution of the resulting geometrical error is shown in
Fig. 9.14. The maximum error is about 1
.
5 pixels, while the mean geometric
error (warping index
[36]) over the total of the brain is about 0
.
4 pixels. We
generally observe that the error is concentrated in areas with little detail in the
image. Other high-contrast regions, such as edges, are resolved much more pre-
cisely than indicated by the value of
, often with subpixel accuracy. On the
other hand, the agreement in the zones with low-contrast is worse and often
only coincidental, since there is little or no information to guide the algorithm.
The evolution of the optimization can be studied from the graphs in Fig. 9.13.
We observe the steady and correlated descent of the observable criterion being
