Biomedical Engineering Reference
In-Depth Information
very first initial guess at each resolution. The distribution is centered on the ini-
tial guess because we want to use the best solution from the lower resolution.
The algorithm restarts until the absolute correlation coefficient between the
reference and registered volumes is above a threshold or the maximum number
of restarts is reached. The perturbation range is
±
5
◦
and
±
5 voxels correspond-
ing to
±
27
.
3 mm,
±
13
.
7mmor
±
6
.
8 mm for resolutions 1
/
4, 1
/
2, or full voxels,
respectively. Absolute CC is used for the restart test rather than MI because of
three reasons: (a) CC has a well-defined range between 0 and 1, (b) CC provides
an independent check of the MI result, and (c) CC has fewer problems with local
and incorrect global maximums for registrations at low resolution far from the
optimum value.
We record all important results following an optimization cycle including
the CC and/or MI values, the number of restarts, and the transformation pa-
rameters. At the end of processing at a lower resolution, we always select
the transformation parameters having the maximum CC value. We then scale
the translation parameters appropriately and assign the new parameters to be
initial values at the next higher resolution. At the highest resolution, we se-
lect the final transformation parameters to be those with the maximum MI
value.
There are several implementation details. We use rigid body transformation
(three translations and three angles) and trilinear interpolation. For optimiza-
tion, we use the downhill simplex method of Nelder and Mead [27]. Optimiza-
tion of alignment ends either when the maximum number of MI calculations is
reached (typically 500) or the fractional change in MI is smaller than a tolerance
(typically 0.001). The very first initial guess at the lowest resolution is all zeros
for the three displacements and three angles. The CC thresholds can be 0.65,
0.70, and 0.75, and the maximum numbers of restarts be 20, 10, and 5, from low
to high resolutions, respectively.
There are several preprocessing details. Isotropic voxels are created using
3D linear interpolation or higher order interpolation methods [20]. From the top
and bottom of the volume, we optionally crop transverse slices that are over
35 mm away from the prostate rim. Cropping is done to remove slices having
reduced brightness due to sensitivity fall off from the receiver coils, artifacts
from a small field of view, displacement of the legs in the treatment position,
and/or bladder deformation.
