Biomedical Engineering Reference
In-Depth Information
Table 10.3:
Average and standard deviation of Tx/Em indirect registration
parameters obtained from the cross-entropy, reversed cross-entropy, and
symmetric divergence registration measures without manual preregistration.
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
.
33
±
1
.
49
0
.
27
±
0
.
99
−
0
.
67
±
0
.
90
0
.
16
±
0
.
47
0
.
05
±
1
.
05
3
.
17
±
1
.
61
6
RCE
3
.
38
±
1
.
37
−
0
.
29
±
1
.
52
−
0
.
77
±
1
.
97
−
0
.
37
±
1
.
13
1
.
21
±
2
.
34
0
.
89
±
3
.
25
5
SD
2
.
35
±
3
.
00
−
0
.
03
±
0
.
37
−
0
.
75
±
1
.
41
−
0
.
13
±
0
.
45
1
.
79
±
2
.
33
−
0
.
41
±
2
.
17
5
compounded and propagated into the indirect computation of the Tx/Em regis-
tration parameters.
Both the reversed cross-entropy and symmetric divergence maximization
failed to register one MR/Tx and one MR/Em case. This resulted in two Tx/Em
cases that could not be registered indirectly for both the techniques. The cor-
responding means and standard deviations for indirectly registered Tx/Em are
listed in Table 10.3. It seems that the reversed cross-entropy and symmetric di-
vergence maximization estimated the z translation parameters more accurately.
For the cross-entropy maximization, the large error in the z translation param-
eter indicates that, among MR/Tx and MR/Em registrations, one overestimates
that parameter and the other underestimates that parameter.
The study of cross-entropy, reversed cross-entropy, and symmetric diver-
gence image registration includes two aspects: (1) the determination if the sim-
ilarity measure is suitable for image registration and (2) how to accurately and
robustly find the optimal registration associated with that measure. The lower
success rates for the reversed cross-entropy and symmetric divergence tech-
niques when registering MR/Tx and MR/Em are not sufficient to reject them as
similarity measures for registration. It may simply indicate that reversed cross-
entropy and symmetric divergence have a very narrow capture range when used
as registration similarity measures. That is, if the initial registration is far away
from the optimal registration, it is hard for the iterative optimization routine to
converge to an optimal solution. As a matter of fact, the angular registration
parameters of MR/Tx and MR/Em can be as large as 30
◦
and the translation pa-
rameters can be as large as 55 mm. To determine if the failed registrations were
caused by the limited capture range, all image pairs were manually registered
and the manual results were used as starting points for iterative optimization.
