We propose to learn a low-dimensional probabilistic deformation model from data which can be used for registration and the analysis of deformations. The latent variable model maps similar deformations close to each other in an encoding space. It enables to compare deformations, generate normal or pathological deformations for any new image or to transport deformations from one image pair to any other image.Our unsupervised method is based on variational inference. In particular, we use a conditional variational autoencoder (CVAE) network and constrain transformations to be symmetric and diffeomorphic by applying a differentiable exponentiation layer with a symmetric loss function. We also present a formulation that includes spatial regularization such as diffusion-based filters. Additionally, our framework provides multi-scale velocity field estimations. We evaluated our method on 3-D intra-subject registration using 334 cardiac cine-MRIs. On this dataset, our method showed state-of-the-art performance with a mean DICE score of 81.2% and a mean Hausdorff distance of 7.3mm using 32 latent dimensions compared to three state-of-the-art methods while also demonstrating more regular deformation fields. The average time per registration was 0.32s. Besides, we visualized the learned latent space and show that the encoded deformations can be used to transport deformations and to cluster diseases with a classification accuracy of 83% after applying a linear projection.

Robust image registration in medical imaging is essential for comparison or fusion of images, acquired from various perspectives, modalities or at different times. Typically, an objective function needs to be minimized assuming specific a priori deformation models and predefined or learned similarity measures. However, these approaches have difficulties to cope with large deformations or a large variability in appearance. Using modern deep learning (DL) methods with automated feature design, these limitations could be resolved by learning the intrinsic mapping solely from experience. We investigate in this paper how DL could help organ-specific (ROI-specific) deformable registration, to solve motion compensation or atlas-based segmentation problems for instance in prostate diagnosis. An artificial agent is trained to solve the task of non-rigid registration by exploring the parametric space of a statistical deformation model built from training data. Since it is difficult to extract trustworthy ground-truth deformation fields, we present a training scheme with a large number of synthetically deformed image pairs requiring only a small number of real inter-subject pairs. Our approach was tested on inter-subject registration of prostate MR data and reached a median DICE score of .88 in 2-D and .76 in 3-D, therefore showing improved results compared to state-of-the-art registration algorithms.