We propose a novel Riemannian framework for analyzing orientation distribution functions (ODFs) in HARDI
data sets, for use in comparing, interpolating, averaging, and denoising ODFs. A recently used Fisher-Rao
metric does not provide physically feasible solutions, and we suggest a modification that removes orientations
from ODFs and treats them as separate variables. This way a comparison of any two ODFs is based on separate
comparisons of their shapes and orientations. Furthermore, this provides an explicit orientation at each voxel
for use in tractography. We demonstrate these ideas by computing geodesics between ODFs and Karcher means of ODFs, for both the original Fisher-Rao and the proposed framework.