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Warping diffusion tensor (DT) fields accurately is much more complicated than that of conventional scalar images. It requires tensors be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Because DT images contain high dimensional information of both spatial orientation and magnitude, standard warping using backward mapping for regular intensity-based images cannot be applied to warp DT images. Therefore, all existing algorithms for warping tensors typically use forward mapping deformations; forward mapping, however, can also create artifacts by failing to define accurately the voxels in the template space where the local deformation is expanding. To overcome this disadvantage, we propose a novel method for the spatial normalization of DT fields that uses a bijection to warp DT datasets from one imaging space to another, without generating artifacts.