Cartesian tensor bases have been widely used to model spherical functions. In medical imaging, tensors of various orders can approximate the diffusivity function at each voxel of a diffusion-weighted MRI data set. This approximation produces tensor-valued datasets that contain information about the underlying local structure of the scanned tissue. The goal in this dissertation is to use the information provided in the tensor field in an automated system that detects changes in the tensor coefficients and correlates them with different types and levels of injury in spinal cord. In order to achieve this, one has to follow several intermediate steps of tensor field processing. These steps include robust estimation of the various orders' diffusion tensor coefficients, tensor field segmentation, registration, and atlas construction as well as extraction of various features, such as anisotropy measures and fiber orientations. Several methods are presented for solving these problems in this dissertation. The proposed algorithms are either the first ever presented in literature for solving a specific problem, or improved alternative solutions to existing techniques. All methods are validated using synthetic simulated diffusion-weighted MR data and their effectiveness is demonstrated in several real datasets. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]