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In this paper, we propose a novel large deformation diffeomorphicregistration algorithm to align high angular resolution diffusion images(HARDI) characterized by orientation distribution functions (ODFs). Ourproposed algorithm seeks an optimal diffeomorphism of large deformation betweentwo ODF fields in a spatial volume domain and at the same time, locallyreorients an ODF in a manner such that it remains consistent with thesurrounding anatomical structure. To this end, we first review the Riemannianmanifold of ODFs. We then define the reorientation of an ODF when an affinetransformation is applied and subsequently, define the diffeomorphic groupaction to be applied on the ODF based on this reorientation. We incorporate theRiemannian metric of ODFs for quantifying the similarity of two HARDI imagesinto a variational problem defined under the large deformation diffeomorphicmetric mapping (LDDMM) framework. We finally derive the gradient of the costfunction in both Riemannian spaces of diffeomorphisms and the ODFs, and presentits numerical implementation. Both synthetic and real brain HARDI data are usedto illustrate the performance of our registration algorithm.

Diffeomorphic Metric Mapping of High Angular Resolution Diffusion Imaging based on Riemannian Structure of Orientation Distribution Functions