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Unsupervised deep-learning (DL) models were recently proposed for deformableimage registration tasks. In such models, a neural-network is trained topredict the best deformation field by minimizing some dissimilarity functionbetween the moving and the target images. After training on a dataset withoutreference deformation fields available, such a model can be used to rapidlypredict the deformation field between newly seen moving and target images.Currently, the training process effectively provides a point-estimate of thenetwork weights rather than characterizing their entire posterior distribution.This may result in a potential over-fitting which may yield sub-optimal resultsat inference phase, especially for small-size datasets, frequently present inthe medical imaging domain. We introduce a fully Bayesian framework forunsupervised DL-based deformable image registration. Our method provides aprincipled way to characterize the true posterior distribution, thus, avoidingpotential over-fitting. We used stochastic gradient Langevin dynamics (SGLD) toconduct the posterior sampling, which is both theoretically well-founded andcomputationally efficient. We demonstrated the added-value of our Basyesianunsupervised DL-based registration framework on the MNIST and brain MRI (MGH10)datasets in comparison to the VoxelMorph unsupervised DL-based imageregistration framework. Our experiments show that our approach provided betterestimates of the deformation field by means of improved mean-squared-error($0.0063$ vs. $0.0065$) and Dice coefficient ($0.73$ vs. $0.71$) for the MNISTand the MGH10 datasets respectively. Further, our approach provides an estimateof the uncertainty in the deformation-field by characterizing the trueposterior distribution.

Unsupervised Deep-Learning Based Deformable Image Registration: A Bayesian Framework