Biomedical Engineering Reference
In-Depth Information
registration parameters. In this chapter, we chose not to report the point differ-
ences.
To further understand the behavior of similarity measures in the vicinity of
an optimal registration, the similarity measures were computed for images in
the neighborhood of a manual registration. It is believed that the manual results
are close to the ground truth. Thus, this calculation would shed light on the
behavior of these measures. To this end, we focused on the MR/Em image pair
of patient B, arbitrarily.
We also evaluated different strategies to cope with the numerical instability
that occurs when maximizing the selected similarity measures. The strategies
were evaluated by inspecting the similarity profiles that resulted from systemati-
cally adjusting the registration parameters from those obtained when the images
underwent manual registration.
10.4.3
Experiment Setup—Minimization
of Similarity Measures
If one has a good estimation of the joint voxel value distribution, then the cross-
entropy, reversed cross-entropy, and symmetric divergence measures can be
minimized to find the optimal registration. Although a reasonably good prior
estimation is difficult to obtain, we report on the outcome of some experi-
ments to validate the idea. We did the experiment on the MR/Em image pair of
Patient B.
The image pair was registered by four clinical experts using an interactive
(manual) registration method. A joint voxel value distribution was calculated
based on the averaged manual registration parameters. This distribution was
then used as the priori. It is worthy to note that the priori probabilities need
to be recomputed for each resolution when the multiresolution optimization is
used. In this test, only two resolution levels were employed, 32 and 64.
To assess the robustness of registration by the cross-entropy, reversed cross-
entropy, and symmetric divergence minimization, two sets of misregistrations
were randomly generated around the above-mentioned average registration re-
sults, and used as initial registrations. In the first set of 100 misregistrations (Set
1), the differences between the rotation angles and the average rotation angles
were uniformly distributed over [
−
10, 10] degrees and the differences between
the translation offsets were uniformly distributed over [
−
10, 10] mm. For the
