Biomedical Engineering Reference
In-Depth Information
terminating step be fractionally smaller than a preset tolerance. In the simplex
optimization, the relative difference between the highest and lowest vertices is
compared against a tolerance (0.0001).
4.2.5.3
Multiresolution Strategies
The above optimization process can be attracted to a local minimum (thus local
maximum of mutual information). To avoid that multiresolution or subsampling
optimization scheme can be used. The idea of multiresolution strategy is simple:
Find the optimal registration on coarse images first. Then using the found solu-
tion as the starting point, find the optimal registration for the fine images. The
coarse images are derived from the original images, by averaging several pixels
in the original images. As a variation of this multiresolution, subsampling is also
used sometimes. Instead of taking the average, a single pixel is picked to form
a coarse image. In the subsampling scheme, the images are never scaled down.
The original images are subsampled periodically, with a gradually increasing
sampling frequency. The optimization result at the lower sampling frequency is
used as the starting point for the higher sampling. Since the images are subsam-
pled, some information is lost.
We propose a multiresolution subsampling scheme. The idea is to combine
the advantages of multiresolution and subsampling. Our experimental results
indicate that this scheme can increase the convergence speed considerably. The
pseudo code for this scheme follows:
For resolution r1 > r2 > ... > rn
Rescale the translation offsets (divided by the
folding number)
Prepare the coarse images
For sampling s1 > s2 ... > sm
Do simplex optimization
Rescale translation offsets to correct different
resolution effect
In the implementation, all these resolutions
r
and sampling frequencies
s
can be
adjusted. In the experimental results reported below, the resolutions are 27, 9,
3, 1 and the sampling frequencies are 3 and 1.
The simplex optimization in the inner loop is identical to the one described
earlier, except the images are scaled down by some folding factor which is equal
