Group action induced averaging for HARDI processing

We consider the problem of processing high angular resolution diffusion images described by orientation distribution functions (ODFs). Prior work showed that several processing operations, e.g., averaging, interpolation and filtering, can be reduced to averaging in the space of ODFs. However, this approach leads to anatomically erroneous results when the ODFs to be processed have very different orientations. To address this issue, we propose a group action induced distance for averaging ODFs, which leads to a novel processing framework on the spaces of orientation (the space of 3D rotations) and shape (the space of ODFs with the same orientation). Experiments demonstrate that our framework produces anatomically meaningful results.