  In this paper, we propose a novel large deformation diffeomorphic
registration algorithm to align high angular resolution diffusion images
(HARDI) characterized by orientation distribution functions (ODFs). Our
proposed algorithm seeks an optimal diffeomorphism of large deformation between
two ODF fields in a spatial volume domain and at the same time, locally
reorients an ODF in a manner such that it remains consistent with the
surrounding anatomical structure. To this end, we first review the Riemannian
manifold of ODFs. We then define the reorientation of an ODF when an affine
transformation is applied and subsequently, define the diffeomorphic group
action to be applied on the ODF based on this reorientation. We incorporate the
Riemannian metric of ODFs for quantifying the similarity of two HARDI images
into a variational problem defined under the large deformation diffeomorphic
metric mapping (LDDMM) framework. We finally derive the gradient of the cost
function in both Riemannian spaces of diffeomorphisms and the ODFs, and present
its numerical implementation. Both synthetic and real brain HARDI data are used
to illustrate the performance of our registration algorithm.
