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NRR algorithms can be divided into two general classes: pairwise and groupwise. Pairwise algorithms register a pair of images at a time. Registration across a group is then achieved by repeated applications of the pairwise algorithm. For example, all images in the training set can be pairwise-registered to some chosen reference example (e.g., [12]). However, this suffers from the general problem that the result obtained depends on the choice of reference. Refinements of this basic approach are possible, where the reference is initialised and updated so as to be representative of the group of images as a whole. The important point to note, however, is that the correspondence for a given training image is defined w.r.t. this reference (which enables consistency of correspondence to be maintained across the group), and the information used in determining the correct correspondence is limited to that contained in that training image and the reference image.
It can be seen that this approach does not take advantage of the full information in the group of images when defining correspondence [21]. Making better use of all the available information is the aim of groupwise registration algorithms, where correspondence is determined across the whole set in a principled manner. One such groupwise method is the Minimum Description Length (MDL) formulation as developed by the authors [16]. The main idea is that the appearance model generated from the current correspondence is made an integral part of the process of further registration, the model being continually updated as the process of registration proceeds. The objective function for this groupwise registration is a description length [22], which considers encrypting the entire training set as a coded message, the length of the message in bits being the objective function. Rather than encoding the raw images, the encoding proceeds by describing each training set image as a series of shape and texture deformations applied to some reference. That is, the encoding explicitly uses the model representation of each image from the appearance model built using the found correspondence. Thus the full encoding must also contain the details of the model itself, and the discrepancy between the actual image and the appearance model representation of that image.
We expect the groupwise approach to give significantly better registration results than the repeated pairwise approach. We compare the performance of two variants of the MDL groupwise approach and a pairwise method. These three algorithms present a suitable test of the discrimination ability of our proposed evaluation framework.
The different NRR algorithms were compared using 2D images, which allowed large-scale experiments to be performed. 104 T1-weighted 3D MR brain images from a dementia study were affinely aligned, and a mid-brain slice extracted from each, at equivalent locations. The set of images was registered using each of the three registration algorithms. An example of one of the resulting models is shown in Figure 12. In each case the specificity and generalisation were computed.