Biomedical Engineering Reference
In-Depth Information
0.16
10000
10000
0.14
100
0.12
ignored
ignored
0.1
1
100
0.08
1
0.06
0.04
0.02
0
−
15
−
10
−
5
0
5
10
15
X Translation (mm)
Figure 10.18: The cross-entropy profiles of an MR/Em image pair in the vicin-
ity of a manual registration when the x-translation changes independently. The
numbers around the profiles indicate the
α
value used to compute a small prob-
ability value which is used to replace zero pdf. Ignored means that those pdfs
are ignored when computing the profile.
similarity-based registration techniques. Therefore, incorporating those mea-
sures to existed packages would be straightforward.
The major problem with applying cross-entropy, reversed cross-entropy, and
symmetric divergence optimziation to image registration is the numerical sta-
bility when the estimated joint pdf or priori joint pdf is zero. If a large sample
of successsful registrations are used to generate the desirable, statistically av-
eraged pdf, it is unlikely that one would have many zero points in the priori
joint pdf. Alternatively, one can assume a parametric form of the priori joint
pdf. The unknown parameters can be estimated from available priori pdf data
points and the pdf can be interpolated at the zero points. Unfortunately, there
is no justification for one parametric form over others, particularly in the multi-
modality cases. To improve its accuracy and robustness, one can also use Paren
