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We consider the problem of aligning high angular resolution diffusion images characterized by orientation distribution functions (ODFs). We cast this problem as an optimization problem where we seek the rotation that aligns the source and target ODFs. This rotation induces a linear transformation of the spherical harmonic coefficients of the ODFs, which can be parametrized by the rotation Euler angles. We propose an algebraic approach to estimate this transformation from a number of ODF correspondences. We evaluate the proposed method on synthetic ODFs as well as on a diffusion MR phantom dataset.