Learning a Probabilistic Model for Diffeomorphic Registration

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.

Unsupervised Probabilistic Deformation Modeling for Robust Diffeomorphic Registration

We propose a deformable registration algorithm based on unsupervised learning of a low-dimensional probabilistic parameterization of deformations. We model registration in a probabilistic and generative fashion, by applying a conditional variational autoencoder (CVAE) network. This model enables to also generate normal or pathological deformations of any new image based on the probabilistic latent space. Most recent learning-based registration algorithms use supervised labels or deformation models, that miss important properties such as diffeomorphism and sufficiently regular deformation fields. In this work, we constrain transformations to be diffeomorphic by using a differentiable exponentiation layer with a symmetric loss function. We evaluated our method on 330 cardiac MR sequences and demonstrate robust intra-subject registration results comparable to two state-of-the-art methods but with more regular deformation fields compared to a recent learning-based algorithm. Our method reached a mean DICE score of 78.3% and a mean Hausdorff distance of 7.9mm. In two preliminary experiments, we illustrate the model's abilities to transport pathological deformations to healthy subjects and to cluster five diseases in the unsupervised deformation encoding space with a classification performance of 70%.