A Symmetric Prior for the Regularisation of Elastic Deformations: Improved anatomical plausibility in nonlinear image registration

Nonlinear registration is critical to many aspects of Neuroimaging research. It facilitates averaging and comparisons across multiple subjects, as well as reporting of data in a common anatomical frame of reference. It is, however, a fundamentally ill-posed problem, with many possible solutions which minimise a given dissimilarity metric equally well. We present a regularisation method capable of selectively driving solutions towards those which would be considered anatomically plausible by penalising unlikely lineal, areal and volumetric deformations. This penalty is symmetric in the sense that geometric expansions and contractions are penalised equally, which encourages inverse-consistency. We demonstrate that this method is able to significantly reduce local volume changes and shape distortions compared to state-of-the-art elastic (FNIRT) and plastic (ANTs) registration frameworks. Crucially, this is achieved whilst simultaneously matching or exceeding the registration quality of these methods, as measured by overlap scores of labelled cortical regions. Extensive leveraging of GPU parallelisation has allowed us to solve this highly computationally intensive optimisation problem while maintaining reasonable run times of under half an hour.