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.

提出了一种基于概率的低维形变模型，可用于图像配准和形变分析，具有对比形变、生成正常或病态形变的能力，以及在多种图像对之间传输形变的能力。在三维心脏 Cine-MRIs 上的实验结果显示出本方法目前显示了最先进的性能。