Diffusion tensor imaging (DTI) can reveal detailed white matter anatomy and has the potential to detect abnormalities in specific white matter structures. Such detection and quantification are, however, not straightforward. The voxel-based analysis after image normalization is one of the most widely used methods for quantitative image analyses. To apply this approach to DTI, it is important to examine if structures in the white matter are well registered among subjects, which would be highly dependent on employed algorithms for normalization. In this paper, we evaluate the accuracy of normalization of DTI data using a highly elastic transformation algorithm, called large deformation diffeomorphic metric mapping. After simulation-based validation of the algorithm, DTI data from normal subjects were used to measure the registration accuracy. To examine the impact of morphological abnormalities on the accuracy, the algorithm was also tested using data from Alzheimer's disease (AD) patients with severe brain atrophy. The accuracy level was measured by using manual landmark-based white matter matching and surface-based brain and ventricle matching as gold standard. To improve the accuracy level, cascading and multi-contrast approaches were developed. The accuracy level for the white matter was 1.88+/-0.55 and 2.19+/-0.84 mm for the measured locations in the controls and patients, respectively.