Given a set of manual segmentations, the aim of this paper is to learn a probability distribution such that samples drawn from that distribution tend to look like manual segmentations of other subjects. This is useful because such a distribution can then be used as a prior in automated segmentation algorithms.

The proposed method extends the usual concept of probabilistic atlases in several ways; for instance, it yields sparse tetrahedral meshes that are less prone to overfitting to the training data than traditional atlases. These atlases are therefore better able to predict the antanomy in unseen subjects, especially when the number of training subjects is small.

A Bayesian modeling approach is used throughout. A first level of inference yields a non-rigid group-wise registration algorithm based on a topology preserving deformation prior; the registration criterion is closely related to the so-called congealing criterion. For higher levels of inference, the method does Bayesian model comparison, which is known to be closely related to the Minimum Description Length principle when Gaussian approximations are used.

The method explicitly aims at finding the optimal deformation regularization, which involves approximating an integral over all possible deformations. An interesting alternative way to do this, proposed by Stephanie Allassonniere and co-workers, is to side-step the integration by sampling from the deformation posterior in an EM algorithm (although you'd still have to approximate the partition function if the deformation model is not Gaussian, as in our case).