Biomedical Engineering Reference
In-Depth Information
Table 10.2:
Average and standard deviation of Tx/Em direct registration
parameters obtained from the cross-entropy (CE), reversed cross-entropy
(RCE), and symmetric divergence (SD) registration measures. The angles are
in degrees, translation offsets in mm
Alg
t
x
t
y
t
z
Success
θ
x
θ
y
θ
z
CE
0
.
64
±
1
.
27
0
.
00
±
0
.
00
0
.
85
±
1
.
71
0
.
21
±
0
.
43
0
.
19
±
0
.
89
−
0
.
98
±
1
.
13
4
RCE
0
.
36
±
1
.
34
0
.
35
±
0
.
63
−
0
.
55
±
1
.
34
−
0
.
14
±
1
.
17
1
.
18
±
1
.
40
1
.
26
±
0
.
69
5
SD
0
.
86
±
1
.
06
0
.
30
±
1
.
53
0
.
14
±
0
.
79
−
0
.
07
±
0
.
92
0
.
79
±
0
.
69
−
0
.
97
±
1
.
39
7
parameters for all successful registrations obtained from the cross-entropy, re-
versed cross-entropy, and symmetric divergence maximization are tabulated in
Table 10.2.
From the data in Table 10.2, one can conclude that registration by the symmet-
ric divergence maximization has the higher success rate. For all cross-entropy,
reversed cross-entropy, and symmetric divergence image registration, the av-
erage differences of the registration parameters from the true parameters are
below the detection thresholds of a trained clinician.
The failed cases of cross-entropy and reversed cross-entropy registration
are intriguing. The diameter of the field of view of the Tx and Em slice images
is 46 cm. A brain with a 20 cm diameter only occupies 1/6 or 1/7 of the slice
area. Thus, in the histogram estimation, many voxel pairs populate in the lowest
bins, which has an adverse effect on the registration. We tried to exclude them
by discarding the low end of the histogram from the similarity measure calcu-
lation and the cross-entropy successfully registered all seven cases, but with
larger mean and standard deviation (data not shown here). Moreover, the same
exclusion scheme reduced the success rate of MR/Tx and MR/Em registration
by cross-entropy maximization. Therefore, no data exclusion techniques were
used in any of the experiments reported in this chapter.
10.5.1.2
Tx/Em Indirect Registration
The Tx and Em images were indirectly registered through the MR images.
Figure 10.2 shows typical MR/Em registration results (of patient B). The ax-
ial, sagittal, and coronal views are overlaid with a changeable transparency.
All three views are correlated by a movable cross-hair token. In the top-left
