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Subsets

The idea here is to speed up the algorithm by essentially pyramiding the whole set (see Figure ) and building up towards a much quicker convergence.

Figure: Illustration of the approach taken when registering using subsets.

This nice hierarchy can allow larger sets to be dealt with, e.g. 50 or even hundreds, something which was thus far impractical. The figure shows how subsets are chosen in the context of image registration to create smaller AAM's. In practice the choice is stochastic although it is now realised that due to the internal intricacies of MATLAB, this arbitrariness results in reduced speed. By registering subsets, a globally good AAM can be constructed. Similar principles can be shown for shapes.

Instead of treating large sets and optimising over these, smaller sets can be handled, thereby reducing the burden of large Eigen analyses. Figures and illustrate that subsets appear to result in better and quicker descent^10.9. The time required to optimise over subsets is surprisingly higher. This issue is a main one for future work.

Figure: Images being registered according to the description length of the entire set of size 10. The X-axis indicates run-time time in seconds.

Figure depicts one typical registration curve showing that the registration quality improves up to a point where betterment is low in extent.

Figure: being registered according to the description length of random subsets of size 4. A choice of subset changes every 10 iterations. It can be seen that the score goes lower, but the time required is then greater.

In can be seen in Figure that a subset-driven approach is slower though it is able to bring about some great improvements after an initial instability at the start. That slow start can be explained by pointing out that an insufficient number of different subset choices was cycled through. As a result, a rather localised optimisation is performed while the overall set benefits very little.