Probabilistic inference of regularisation in non-rigid registration

A long-standing issue in non-rigid image registration is the choice of the level of regularisation. Regularisation is necessary to preserve the smoothness of the registration and penalise against unnecessary complexity. The vast majority of existing registration methods use a fixed level of regularisation, which is typically hand-tuned by a user to provide "nice" results. However, the optimal level of regularisation will depend on the data which is being processed; lower signal-to-noise ratios require higher regularisation to avoid registering image noise as well as features, and different pairs of images require registrations of varying complexity depending on their anatomical similarity. In this paper we present a probabilistic registration framework that infers the level of regularisation from the data. An additional benefit of this proposed probabilistic framework is that estimates of the registration uncertainty are obtained. This framework has been implemented using a free-form deformation transformation model, although it would be generically applicable to a range of transformation models. We demonstrate our registration framework on the application of inter-subject brain registration of healthy control subjects from the NIREP database. In our results we show that our framework appropriately adapts the level of regularisation in the presence of noise, and that inferring regularisation on an individual basis leads to a reduction in model over-fitting as measured by image folding while providing a similar level of overlap.