Geometric Deep Learning for Unsupervised Registration of Diffusion Magnetic Resonance Images.

Deep learning based models for registration predict a transformation directly from moving and fixed image appearances. These models have revolutionized the field of medical image registration, achieving accuracy on-par with classical registration methods at a fraction of the computation time. Unfortunately, most deep learning based registration methods have focused on scalar imaging modalities such as T1/T2 MRI and CT, with less attention given to more complex modalities such as diffusion MRI.

VolterraNet: A Higher Order Convolutional Network With Group Equivariance for Homogeneous Manifolds.

Convolutional neural networks have been highly successful in image-based learning tasks due to their translation equivariance property. Recent work has generalized the traditional convolutional layer of a convolutional neural network to non-euclidean spaces and shown group equivariance of the generalized convolution operation. In this paper, we present a novel higher order Volterra convolutional neural network (VolterraNet) for data defined as samples of functions on Riemannian homogeneous spaces.

ManifoldNet: A Deep Neural Network for Manifold-Valued Data With Applications.

Geometric deep learning is a relatively nascent field that has attracted significant attention in the past few years. This is partly due to the availability of data acquired from non-euclidean domains or features extracted from euclidean-space data that reside on smooth manifolds. For instance, pose data commonly encountered in computer vision reside in Lie groups, while covariance matrices that are ubiquitous in many fields and diffusion tensors encountered in medical imaging domain reside on the manifold of symmetric positive definite matrices.