Principal Geodesic Analysis on Symmetric Spaces: Statistics of Diffusion Tensors

Diffusion tensor magnetic resonance imaging (DT-MRI) is emerging as an important tool in medical image analysis of the brain. However, relatively little work has been done on producing statistics of diffusion tensors. A main difficulty is that the space of diffusion tensors, i.e., the space of symmetric, positivedefinite matrices, does not form a vector space. Therefore, standard linear statistical techniques do not apply. We show that the space of diffusion tensors is a type of curved manifold known as a Riemannian symmetric space. We then develop methods for producing statistics, namely averages and modes of variation, in this space. In our previous work we introduced principal geodesic analysis, a generalization of principal component analysis, to compute the modes of variation of data in Lie groups. In this work we expand the method of principal geodesic analysis to symmetric spaces and apply it to the computation of the variability of diffusion tensor data. We expect that these ...

• Type: Conference
• Year: 2004
• Where: ECCV
• Authors: P. Thomas Fletcher, Sarang C. Joshi
• Keywords: Computer Vision, Diffusion Tensor, Diffusion Tensor Data, Diffusion Tensor Magnetic Resonance Imaging, ECCV 2004