Diffusion Tensor Field Registration in the Presence of Uncertainty

We propose a novel method for deformable tensor-to-tensor registration of Diffusion Tensor Imaging (DTI) data. Our registration method considers estimated diffusion tensors as normally distributed random variables whose covariance matrices describe uncertainties in the mean estimated tensor due to factors such as noise in diffusion weighted images (DWIs), tissue diffusion properties, and experimental design. The dissimilarity between distributions of tensors in two different voxels is computed using the Kullback-Leibler divergence to drive a deformable registration process, which is not only affected by principal diffusivities and principal directions, but also the underlying DWI properties. We in general do not assume the positive definite nature of the tensor space given the pervasive influence of noise and other factors. Results indicate that the proposed metric weights voxels more heavily whose diffusion tensors are estimated with greater certainty and exhibit anisotropic diffusion behavior thus, intrinsically favoring coherent white matter regions whose tensors are estimated with high confidence.