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This paper presents a novel method for diffusion MRI registration that treats the diffusion profile as an arbitrary positive-valued function of spatial direction and treats Cartesian diffusion tensors as a special case. A metric based on elementary notions of signal analysis is presented and in the case of diffusion tensors, a closed form expression of the metric is derived in terms of tensor components. The registration method applies piece-wise local affine registration in a multi-resolution framework. Affine registration is defined in terms of an objective function that allows derivatives to be computed analytically. Experimental results demonstrate the robustness of the method for non-linear registration.