1. National Alliance for Medical Image Computing http://na-mic.org Utah DTI Research Differential Geometry for DTI analysis Descriptive statistics of DTI Hypothesis testing DTI Interpolation and filtering of DTI

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

3. National Alliance for Medical Image Computing http://na-mic.org Descriptive Statistics Averages and Modes of Variation Preserves natural properties –Positive eigenvalues –Tensor Orientation –Tensor Size (determinant) Prototype implemented in ITK

4. National Alliance for Medical Image Computing http://na-mic.org Hypothesis Testing Tests differences in diffusion tensors from two groups Uses full six-dimensional information from tensors Prototype implemented in ITK Upcoming IPMI submission

5. National Alliance for Medical Image Computing http://na-mic.org Interpolation and Filtering Interpolation of tensors –Based on weighted averages in curved geometry Filtering –Anisotropic filtering based on curved geometry Implementation in progress

6. National Alliance for Medical Image Computing http://na-mic.org 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

7. National Alliance for Medical Image Computing http://na-mic.org 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