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In this paper, we extend a new registration framework from scalar image to diffusion tensor image. As the extension from scalar to tensor image is non-trivial, we write the process in detail. The registration framework is based on polynomial expansion transform. The idea of polynomial expansion is that the image is locally approximated by polynomials at each pixel. Registration algorithms are developed for affine model by observing the changes between source and target images locally, from their polynomial expansion coefficients. Experiments are tested on human diffusion tensor images.