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Comparing Different Methods of NRR

A common task in medical image analysis is the estimation of correspondences across a group of images, to allow mapping of effects into a common co-ordinate frame when performing population studies. A widely used approach is to use a non-rigid registration algorithm to map a chosen reference image onto each example, defining the correspondence across the group [12]. However, it has been argued [4] that this pairwise approach does not take advantage of the full information in the group, and thus may lead to sub-optimal registration. We have been investigating groupwise methods of registration which aim to make the best use of the group as a whole when estimating the correspondence. We work within a minimum description length (MDL) framework. The aim is to construct a statistical appearance model which can exactly synthesize each example in the training set as efficiently as possible [17]. It has been observed that the more the compact the representation, the better the correspondences. The general approach is to define a deformation field between reference frame and each training image. For a given choice of sets of fields, one can compute the cost of encoding the images (a combination of the coding cost of the model, the cost of the parameters and the cost of residuals between the synthesized images and the training images). The effect on this total description length of modifying the deformation fields can be evaluated - the correspondence problem becomes a (very high dimensional) optimisation problem. Within this general framework we compare three different approaches (for details see [17]):

1. Pairwise registration, using the first image as a reference
2. Groupwise registration in which the reference model is just the current mean of the shape and intensities across the training set, and no constraints are placed on the deformations
3. Groupwise registration to the mean including a term encouraging a compact representation of the set of deformations.

Though the algorithms will work in 3D, for the evaluation experiments we concentrate on a 2D implementation (allowing more large-scale experiments to be performed). We have a dataset of 104 3D MR images of normal brains , which have been affine aligned and a single slice at equivalent location extracted from each. Fig. 5 (left) shows examples of extracted slices. In order to evaluate the different registration algorithms outlined above, we register the 104 2D slices using the different techniques, construct statistical models from them and calculate the specificity and generalisation measures.