Segmenting Fiber Bundles in Diffusion Tensor Images

We consider the problem of segmenting fiber bundles in diffusion tensor images. We cast this problem as a manifold clustering problem in which different fiber bundles correspond to different submanifolds of the space of diffusion tensors. We first learn a local representation of the diffusion tensor data using a generalization of the locally linear embedding (LLE) algorithm from Euclidean to diffusion tensor data. Such a generalization exploits geometric properties of the space of symmetric positive semi-definite matrices, particularly its Riemannian metric. Then, under the assumption that different fiber bundles are physically distinct, we show that the null space of a matrix built from the local representation gives the segmentation of the fiber bundles. Our method is computationally simple, can handle large deformations of the principal direction along the fiber tracts, and performs automatic segmentation without requiring previous fiber tracking. Results on synthetic and real diffusion tensor images are also presented.