Segmentation of High Angular Resolution Diffusion MRI Using Sparse Riemannian Manifold Clustering

We address the problem of segmenting high angular resolution diffusion imaging (HARDI) data into multiple regions (or fiber tracts) with distinct diffusion properties. We use the orientation distribution function (ODF) to model diffusion and cast the ODF segmentation problem as a clustering problem in the space of ODFs. Our approach integrates tools from sparse representation theory and Riemannian geometry into a graph theoretic segmentation framework. By exploiting the Riemannian properties of the space of ODFs, we learn a sparse representation for each ODF and infer the segmentation by applying spectral clustering to a similarity matrix built from these representations. In cases where regions with similar (resp. distinct) diffusion properties belong to different (resp. same) fiber tracts, we obtain the segmentation by incorporating spatial and user-specified pairwise relationships into the formulation. Experiments on synthetic data evaluate the sensitivity of our method to image noise and to the concentration parameters, and show its superior performance compared to alternative methods when analyzing complex fiber configurations. Experiments on phantom and real data demonstrate the accuracy of the proposed method in segmenting simulated fibers and white matter fiber tracts of clinical importance.