Biomedical Engineering Reference
In-Depth Information
Table 10.4:
Average and standard deviation of Tx/Em indirect registration
parameters obtained from the cross-entropy, reversed cross-entropy, and
symmetric divergence registration measures with manual pre-registration.
The angles are in degrees and translation offsets in mm
Alg
t
x
t
y
t
z
Success
θ
x
θ
y
θ
z
CE
2
.
26
±
1
.
06
0
.
64
±
0
.
81
0
.
31
±
1
.
23
0
.
45
±
0
.
25
0
.
34
±
0
.
77
−
3
.
69
±
2
.
46
7
RCE
2
.
55
±
1
.
06
1
.
29
±
1
.
16
1
.
40
±
2
.
26
0
.
76
±
2
.
02
1
.
91
±
2
.
34
0
.
78
±
2
.
01
7
SD
1
.
79
±
1
.
21
0
.
91
±
1
.
80
1
.
32
±
2
.
27
0
.
70
±
1
.
91
1
.
70
±
2
.
00
−
0
.
27
±
2
.
69
7
The results of mean and standard deviation for indirect Tx/Em registrations are
tabulated in Table 10.4. Again, the large error in the z translation parameter for
the cross-entropy maximization indicates that, among MR/Tx and MR/Em reg-
istrations, one overestimates that parameter and the other underestimates that
parameter.
As can be seen, all three similarity measures successfully registered seven
MR/Tx and seven MR/Em cases with a manual prealignment, and the means and
standard deviations are comparable to those in Table 10.3. As a comparison, the
Tx/Em indirect registration parameters were also computed from manual MR/Tx
and MR/Em registration. The mean and standard deviation of the Tx/Em indi-
rect registration parameters were (2
.
42
±
2
.
69
,
0
.
22
±
2
.
20
,
0
.
15
±
2
.
50
,
2
.
66
±
1
.
94
,
0
.
69
±
2
.
01
,
2
.
31
±
3
.
14). Since most of the manual registration results had
zeros in the
y
- and
z
-axis rotation, the mean values of these parameters are small.
Thus, a small mean does not necessarily mean that the manual registration is
more accurate. Since the reversed cross-entropy and symmetric divergence reg-
istration has a small capture range, one might be concerned that their registration
results would not deviate significantly from the manual starting registration. If
this were true, the mean and standard deviation values in Table 10.4 would re-
flect the mean and standard deviation associated with the manual registration
results. To check this possible situation, the difference of the cross-entropy,
reversed cross-entropy, and symmetric divergence registration results and the
manual starting solutions was checked. The angle difference was as large as
5
◦
and the translation was as large as 6 mm. Thus, it is unlikely that the mean
and standard deviation for the reversed cross-entropy and symmetric diver-
gence registration merely reflect the mean and standard deviation in the manual
registration.
