Registration of Spherical Functions from High Angular Resolution Diffusion Imaging using the Heat Kernel Signature and Möbius Transformation

High angular resolution diffusion imaging (HARDI) is a powerful variant of diffusion MRI, which images the 3D profile of diffusion at each imaged location in the brain. At each voxel, this leads to an orientation density function (ODF) expressing the probability density of water diffusion in each direction on the unit sphere. As diffusion is greatest along the brain’s axons, these functions are used to map fiber trajectories (tractography) and fiber integrity. To average and compare this data across subjects, we developed a new method based on the heat kernel signature and ‘Möbius voting’ to identify and align peaks of diffusivity on the sphere. We compare our method to standard coordinate-based averaging, and it helps to reinforce consistent features in both synthetic data and real HARDI data. This scheme to compare and integrate HARDI data may be helpful in population-based analyses of brain integrity and connectivity.