Biomedical Engineering Reference
In-Depth Information
The algorithm always gave very nearly the same transformation parameters
(
<
0
.
01 voxels and 0.01
◦
) for the 17 volume pairs in this study using a wide va-
riety of initial guesses. We also found that MI was more accurate than CC at
the highest resolution [1]. Second, the multiresolution approach enabled the
program to get close to the final value quickly because of the reduced number
of calculations. That is, the time for reformatting at the lowest resolution of 1/4
number of voxels in a linear dimension was 0.16 minute, less than 1/63 times
that at the highest resolution, a value nearly equal to the 1/64 expected from the
change in the number of voxels. In a typical example, the number of restarts
was 5, 1, and 1 for resolutions at 1/4, 1/2, and the full number of voxels in a linear
dimension, respectively. When we checked the restarts at the resolution of 1/4
number of voxels, we determined that none of the five restarts converged to the
same transformation. It has been our experience that more restarts are desirable
at the lower resolutions, and the algorithm includes this feature. Each call to
the Simplex optimization resulted in 50 to 100 MI evaluations before the toler-
ance (0.001) was reached. In some experiments on multiple volumes, we reduced
the tolerance value but found little difference in registration quality, probably
because of the restarting and multiresolution features. The time for rigid body
registration, typically 5-10 min on a Pentium IV, 1.8 GHz CPU, with 1.0 GB of
memory, could possibly be reduced to within one minute with optimized C code
rather than the high level language IDL.
Some technical aspects of non-rigid registration are of interest. Fig. 3.16
shows the optimization time and MI values between registered volumes as a
function of VOI size. The optimization time for 180 CPs increases roughly linearly
with the number of voxels within a VOI, about 0.5 minutes for VOIs with 16 voxels
on one side and 30 minutes for VOIs with 64 voxels on a side. In Fig. 3.16, the MI
curve saturates at the VOI size of 64 voxels on a side which means the size of 64
gave better MI value. These curves are for the case of treatment-diagnosis for
volunteer S2. When we examined the cases of full-empty bladder and volumes
acquired over one week time interval, we found that the VOI size of 16 voxels
on a side worked best. Using the same computer above, for a volume with
256
×
256
×
140 voxels and 180 CPs, the non-rigid registration typically takes
about 15-45 minutes depending on the VOI size.
We report some details on VOI optimization for a typical treatment-
diagnosis volume pair from subject S2. Following rigid body registration, the
mean distance between the manually selected reference and floating CPs was
