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We present a variational framework for the registration of tensor-valued images. It is based on an energy functional with four terms: a data term based on a diffusion tensor constancy constraint, a compatibility term encoding the physical model linking domain deformations and tensor reorientation, and smoothness terms for deformation and tensor reorientation. Although the tensor deformation model employed here is designed with regard to diffusion tensor MRI data, the separation of data and compatibility term allows to adapt the model easily to different tensor deformation models. We minimise the energy functional with respect to both transformation fields by a multiscale gradient descent. Experiments demonstrate the viability and potential of this approach in the registration of tensor-valued images.