Diffusion Tensor Imaging is a type of Magnetic Resonance Imaging that allows for the examination of brain connectivity and axonal integrity. Diffusion Tensor Images are created by capturing Diffusion-Weighted MRI images with specific RF pulses, inputing the images and the RF pulse gradient vectors into a set of equations, and solving the equations with linear algebra. To compare one DTI image with another, the images can be aligned using Image Registration. Image Registration works by defining a metric that describes the similarity between two images and iteratively transforming one of the images until the similarity measure is minimized. Existing methods of DTI comparison fit tensors to DW-MRI images, compute matrix logarithms to transform the tensors into a vector-space, register the vector-space structures, and then matrix exponentiate the results to transform them back to tensors. Logging and exponentiating the tensors introduces biases and noise so this registration framework is not ideal. Additionally, the information encoded in a diffusion tensor is a subset of the information present in the original DW-MRI images. This thesis proposes a new registration framework which avoids these shortcomings by registering the underlying DW-MRI images and then fitting the diffusion tensors to the registered DW-MRI images and transformed gradient vectors. The existing DTI registration framework and the new DW-MRI registration framework are applied to a small image set and their results are compared along a number of qualitative and quantitative attributes.
Applied and Computational Mathematics (MS)
Department, Program, or Center
School of Mathematical Sciences (COS)
Tuttle, Kevin, "Registration of Diffusion Tensor Images in Log-Euclidean and Euclidean Space" (2019). Thesis. Rochester Institute of Technology. Accessed from
RIT – Main Campus