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 [11]. However, it has been argued [3]
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 [16]. 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 [16]):

- Pairwise registration, using the first image as a reference
- 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
- Groupwise registration to the mean including a term encouraging a compact representation of the set of deformations