Biomedical Engineering Reference
In-Depth Information
Table 10.5:
Average and standard deviation of MR/Em registration parameters
obtained from cross-entropy, reversed cross-entropy, and symmetric
divergence minimization. The angles are in degrees and translation offsets in
mm
Alg
t
x
t
y
t
z
Success
θ
x
θ
y
θ
z
Set 1
CE
0
.
03
±
0
.
80
0
.
18
±
0
.
74
−
0
.
13
±
0
.
44
0
.
03
±
0
.
13
−
0
.
02
±
0
.
42
−
0
.
04
±
0
.
17
46%
RCE
−
0
.
05
±
0
.
45
0
.
09
±
0
.
39
0
.
07
±
0
.
31
0
.
07
±
0
.
33
0
.
06
±
0
.
31
−
0
.
01
±
0
.
10
53%
SD
0
.
00
±
0
.
10
0
.
06
±
0
.
34
0
.
05
±
0
.
29
0
.
05
±
0
.
30
0
.
02
±
0
.
13
−
0
.
02
±
0
.
11
68%
Set 2
CE
0
.
23
±
1
.
04
0
.
24
±
0
.
87
0
.
02
±
0
.
51
0
.
10
±
0
.
50
−
0
.
07
±
0
.
59
−
0
.
11
±
0
.
29
41%
RCE
0
.
02
±
0
.
29
0
.
10
±
0
.
43
0
.
04
±
0
.
35
0
.
06
±
0
.
38
0
.
00
±
0
.
33
−
0
.
03
±
0
.
14
51%
SD
−
0
.
06
±
0
.
51
−
0
.
02
±
0
.
33
0
.
06
±
0
.
30
0
.
00
±
0
.
31
0
.
06
±
0
.
48
−
0
.
01
±
0
.
10
52%
using the average manual registration parameters, as mentioned earlier. Refer
to section 10.4.3 for details on the experimental setup.
Table 10.5 lists the statistics of the registration results for two sets of ex-
periments. As the table reveals, the registration parameters are very close to
those of the manual results and the differences of these registration parameters
are well below the detection threshold of a trained technician. This is expected
since the priori was calculated based on the manual registration results. Also
revealed by Table 10.5 is that both reversed cross-entropy and symmetric diver-
gence outperformed cross-entropy minimization in terms of success rate, and
that symmetric divergence has the highest overall success rate.
Note that the implementation of this minimization process is not yet opti-
mized, e.g., one may use Paren density estimation with a Gaussian kernel to add
some smoothness and stability to the similarity functions. Nevertheless, these
results indicate that cross-entropy, reversed cross-entropy, and symmetric diver-
gence minimization can yield a very good registration if a good prior estimation
is available.
10.5.2.2
Behavior Around True Registration
The behavior of these three similarity measures was also checked in the vicinity
of the manual registration, with the desirable prior calculated from that same
manual registration.
