Optimisation

The nature of the image registration problem means that the search space for any optimisation algorithm is typically very high dimensional. In many cases, a general optimiser is used to solve the problem. In other cases, a more problem-specific optimiser is devised. In the case of free-form deformations, for example, the optimisation is simple because it is possible to deal with just one parameter at a time. In the case of fluid registration, the derivative of the objective function, which is indicative of force, is used to drive the fluid flow. It is apparent that the warp representation, whether it is based on fluid, FFD, or even basis functions, affects the choice of optimisation method. A standard optimiser - even though it might be effective - simply does not take advantage of the nature of the warp representation and the data at hand.

Suggestions have been made over the years with regard to the issue of speeding up similarity measures and NRR in general []. The above measures depend heavily, especially from an efficiency point-of-view, on the dimensions of an image. A multi-resolution approach [] has an abundance to offer in this case. For example:

It can be used to speed up the entire process. Blurring or averaging, followed by re-sampling or sub-sampling, allows images of smaller size to be manipulated and complexity to be quadratically lessened. As the similarity measures are proportional to the size of images, far better performance can be attained with transition from coarse to finer resolution. Pluim et al. [] studied the effects that this approach will have on the measurement of similarity.
A multi-resolution approach has other advantages, such as its ability to make the optimiser avoid local minima.

Roy Schestowitz 2010-04-05