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Discussion
This paper has examined the problem of optimisation for fully automatic
registration of brain images. In particular, the problem of avoiding
local minima is addressed in two ways. Firstly, a general
apodization (smoothing) method was formulated for cost functions in
order to eliminate small discontinuities formed by discontinuous
changes of the number of voxels in the overlapping field of view with
changing transformation parameters. Secondly, a novel hybrid
global-local optimisation method was proposed which uses prior
knowledge about the problem (size of the brain, expected
changes in scalings, etc.) while combining the speed of local
optimisation with an initial search phase and multi-start optimisation
component. The latter two components are similar to those used in
Simulated Annealing and Genetic Algorithms -- two popular, but slow,
global optimisation techniques.
Only affine (linear) registration was examined in this paper as,
although this is a much easier problem than general non-linear
registration, finding the global minimum is still difficult.
Furthermore, many non-linear methods rely on an initial affine
registration to find a good starting position, and so having a good
method of affine registration is important.
The global optimisation method proposed here does not, however,
guarantee finding the global minimum. This is typical though, as even
methods such as Simulated Annealing and Genetic Algorithms only
provide a statistical guarantee which cannot be met in practice. The
results, though, are encouraging, and by using finer search grids, the
likelihood of finding the global minimum can be increased. This
requires that there be sufficient time at hand, or a sufficiently fast
computer. However, even with modest resources this method can find
the global minimum and solve the registration problem within one hour
(and often much less) more reliably than the other methods tested.
Optimisation is only one aspect of the registration problem, although
it is practically a very important one. Other aspects such as interpolation,
alternative cost functions and understanding the properties of existing
cost functions remain important areas for further work. In addition,
a theoretical justification for the current method and finding a method
suitable for higher dimensional transformations are
important areas for future research.
The implementations of the registration and motion correction methods
(FLIRT and MCFLIRT) were tested using experiments designed to demonstrate
the improved robustness and accuracy. These issues are important and
each is examined separately.
Subsections
Next: Robustness Study
Up: tr02mj1
Previous: Real Activation Study
Peter Bannister
2002-05-03