Biomedical Engineering Reference
In-Depth Information
-
h
(
x
) -
g
1
Inverse Consistency Error
(
x
)
CL-TPS
CI-TPS
CLI-TPS
Figure 6.10:
Images that display the magnitude and location of forward trans-
formation inverse consistency errors for matching data sets
B
2 and
B
5 with
UL-TPS, CL-TPS, CI-TPS, and CLI-TPS registration algorithms.
bright pixels in the other images. This figure shows that consistent registration
algorithms produced forward and reverse transformations that had sub-voxel
inverse consistency errors at all voxel locations. The inverse consistent errors
in the UL-TPS and CL-TPS algorithms are greatest away from the landmark driv-
ing forces because the landmark driving forces are implicitly inverse consistent.
The largest inverse consistency errors in the CI-TPS and CLI-TPS algorithms
occur near edges where there is a correspondence ambiguity associated with
the intensity matching solution.
Table 6.2 summarizes the representative statistics collected from the exper-
iments. Comparing the results of the UL-TPS and CL-TPS algorithms shows that
the addition of inverse consistency constraint (ICC) improved the inverse con-
sistency of the transformations with no degradation of the landmark matching.
Note that for the UL-TPS algorithm, the inverse consistency error tends to be
larger as one moves away from landmarks and that the inverse consistency error
can be decreased by defining more corresponding landmarks.
Table 6.2 also demonstrates that the CI-TPS and CLI-TPS registrations have
a smaller average intensity difference but larger landmark errors. The CLI-
TPS has smaller average intensity difference and smaller landmark errors than
the CI-TPS registration algorithm. The CLI-TPS algorithm produces a better
similarity match because the landmark driving force pulls the intensity driv-
ing function out of local minima. It should be noted that the large number
of landmarks used in the CLI-TPS registration limits the effect of the inten-
sity driving force in neighborhoods of the landmarks. In practice, when the
