A Riemannian Framework for Orientation Distribution Function Computing

Compared with Diffusion Tensor Imaging (DTI), High Angular Resolution Imaging (HARDI) can better explore the complex microstructure of white matter. Orientation Distribution Function (ODF) is used to describe the probability of the fiber direction. Fisher information metric has been constructed for probability density family in Information Geometry theory and it has been successfully applied for tensor computing in DTI. In this paper, we present a state of the art Riemannian framework for ODF computing based on Information Geometry and sparse representation of orthonormal bases. In this Riemannian framework, the exponential map, logarithmic map and geodesic have closed forms. And the weighted Frechet mean exists uniquely on this manifold. We also propose a novel scalar measurement, named Geometric Anisotropy (GA), which is the Riemannian geodesic distance between the ODF and the isotropic ODF. The Renyi entropy $H_{1/2}$ of the ODF can be computed from the GA. Moreover, we present an A...

• Type: Conference
• Year: 2009
• Where: MICCAI
• Authors: Jian Cheng, Aurobrata Ghosh, Tianzi Jiang, Rachid Deriche
• Keywords: HARDI, Information Geometry, Interpolation, Log-euclidean Riemannian Metric, Medical Imaging, MICCAI2009, Orientation Distribution Function, Orthonormal Basis, Riemannian Framework, Riemannian Mean