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Methods of Speedup

There are several tricks-of-the-trade, which can be used to speed up the process of registration assessment and model evaluation in 3-D. A few examples follow.

Multi-scale. One strategy, for example, involves resampling the data, then dealing with smaller (downsized) versions of the whole, as shown in Figure [*]. The basic concept is that, if the scale of the problem is reduced, it can be handled at a coarse level and then iteratively handled at finer levels, until the original unscaled data is reached.

Figure: A multi-resolution approach illustrated in 2-D. Coarser representations are shown at the top levels and the original image lies at the bottom.
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Improving optimisation and reducing complexity. Chapter 5 described a method for registering sets of images and refining a model using optimisation, whereas subsequent chapters described a method for assessing a registration by repeated computation. In both cases, an answer is available only once the process is completed and further analysis takes place. Some of the information derived relates to locality of variation, so it's worth taking advantage of it.
A strategy worth employing and exploring is one which uses figures of merit, e.g. model properties or Specificity, to also affect decisions that are made by the algorithm and place focus on areas of greater significance (containing increased variation for example). In practice, it is possible to divide the problem into a set of smaller ones. This means that a box of voxels may be sliced into 8 ($2^{3}$) equal-sized boxes which are then used in the analysis, or even more usefully, the box should be rescaled to become 8 times smaller in terms of volume and then dealt with separately.

Selective assessment of slices. In general, there is not much which distinguishes the method's use in 2-D and in 3-D, other than efficiency factors. However, several possibilities emerge owing to the fact that 3-D data can be interpreted differently once its dimensionality is reduced. For example, one can choose one representative slice from a larger volume and refine the evaluation by considering more slices, one at a time. This suffers from the fact that voxels whose position varies in the third dimension, i.e. it moves between the slices due to warping, will not be treated appropriately. All these issues, along with other pitfalls, will be addressed in the near future.

Roy Schestowitz 2010-04-05