Bundle Geodesic Convolutional Neural Network for DWI Segmentation from Single Scan Learning

We present a tissue classifier for Magnetic Resonance Diffusion Weighted Imaging (DWI) data trained from a single subject with a single b-value. The classifier is based on a Riemannian Deep Learning framework for extracting features with rotational invariance, where we extend a G-CNN learning architecture generically on a Riemannian manifold. We validate our framework using single-shell DWI data with a very limited amount of training data - only 1 scan. The proposed framework mainly consists of three layers: a lifting layer that locally represents and convolves data on tangent spaces to produce a family of functions defined on the rotation groups of the tangent spaces, i.e., a section of a bundle of rotational functions on the manifold; a group convolution layer that convolves this section with rotation kernels to produce a new section; and a projection layer using maximisation to collapse this local data to form new manifold based functions. We present an instantiation on the 2-dimensional sphere where the DWI orientation data is in general represented, and we use it for voxel classification. We show that this allows us to learn a classifier for cerebrospinal fluid (CSF) - subcortical - grey matter - white matter classification from only one scan.