Biomedical Engineering Reference
In-Depth Information
0.08
10000
10000
0.07
0.06
100
0.05
100
ignored
0.04
ignored
1
0.03
1
0.02
0.01
0
−
15
−
10
−
5
0
5
10
15
X Rotation (degrees)
Figure 10.17: The cross-entropy profiles of an MR/Em image pair in the vicin-
ity of a manual registration when the x-rotation angle changes independently.
The numbers around the profiles indicate the
α
value used to compute a small
probability value which is used to replace zero pdf. The profile that is labelled
“ignored” represents the case where the contribution from zero joint pdfs was
ignored in the profile computation.
registration are independent of each other. This priori joint pdf is not favorable
since the voxel values in two different images reflect the physical properties
of the same object and thus they are most likely related in some way, at least
from a statistical point of view. If more than one likely and unlikely priori pdf
is available, one can define cross-entropy, reversed cross-entropy, and symmet-
ric divergence for them and maximize or minimize them collectively, where a
multiobjective optimization approach would be useful, as already illustrated in
Zhu [18].
The overall flow chart for the three similarity measures as applied to im-
age registration is presented for both maximization and minimization cases.
It shall be noted that this flow chart is also consistent with those of most
