This paper presents a novel affine registration algorithm for diffusion tensor images. The proposed metric derived from the standpoint of diffusion profiles not only has concrete physical underpinning but also can be extended for comparing higher-order diffusion models. The non-translational part of the affine transformation is parametrized in the spirit of the Polar Decomposition Theorem. The registration objective function and its derivatives are derived analytically by combining this parametrization scheme with finite strain tensor reorientation. The affine algorithm is embeded in a multi-resolution piecewise affine framework for non-rigid registration.