Symmetric Positive-Definite Cartesian Tensor Orientation Distribution Functions (CT-ODF) [chapter]

Yonas T. Weldeselassie, Angelos Barmpoutis, M. Stella Atkins
2010 Lecture Notes in Computer Science  
A novel method for estimating a field of orientation distribution functions (ODF) from a given set of DW-MR images is presented. We model the ODF by Cartesian tensor basis using a parametrization that explicitly enforces the positive definite property to the computed ODF. The computed Cartesian tensors, dubbed Cartesian Tensor-ODF (CT-ODF), are symmetric positive definite tensors whose coefficients can be efficiently estimated by solving a linear system with non-negative constraints.
more » ... , we show how to use our method for converting higher-order diffusion tensors to CT-ODFs, which is an essential task since the maxima of higher-order tensors do not correspond to the underlying fiber orientations. We quantitatively evaluate our method using simulated DW-MR images as well as a real brain dataset from a post-mortem porcine brain. The results conclusively demonstrate the superiority of the proposed technique over several existing multi-fiber reconstruction methods.
doi:10.1007/978-3-642-15705-9_71 fatcat:llbampkezzfcnavrw7g5op66cq