National Alliance for Medical Image Computing Utah DTI Research Differential Geometry for DTI analysis Descriptive statistics of DTI Hypothesis testing DTI Interpolation and filtering of DTI

National Alliance for Medical Image Computing Natural geometry for tensor analysis Enforces positive eigenvalues Basis for statistics, interpolation, and processing Space of 2x2 tensors: Curved Tensor Geometry

National Alliance for Medical Image Computing Descriptive Statistics Averages and Modes of Variation Preserves natural properties –Positive eigenvalues –Tensor Orientation –Tensor Size (determinant) Prototype implemented in ITK

National Alliance for Medical Image Computing Hypothesis Testing Tests differences in diffusion tensors from two groups Uses full six-dimensional information from tensors Prototype implemented in ITK Upcoming IPMI submission

National Alliance for Medical Image Computing Interpolation and Filtering Interpolation of tensors –Based on weighted averages in curved geometry Filtering –Anisotropic filtering based on curved geometry Implementation in progress

National Alliance for Medical Image Computing StatisticsProcessing Software TensorGeometry LinearGeometry CurvedGeometry Other? DescriptiveStats TensorGeometry HypothesisTests TensorGeometry Interpolation TensorGeometry Filtering TensorGeometry Different tensor geometries can be defined Each package can swap in/out different geometries

National Alliance for Medical Image Computing Future Work (6 months) Further develop tensor statistics—make publicly available Build prototypes of tensor filtering and interpolation Continue research into DTI hypothesis testing –Methods –Exploratory Experiments