Symmetric positive-definite cartesian tensor orientation distribution functions (CT-ODF)

Authors:
Yonas T. Weldeselassie;Angelos Barmpoutis;M. Stella Atkins
Affiliations:
School of Computing Science, Simon Fraser University;Dept. of Computer & Information Science and Engineering, University of Florida;School of Computing Science, Simon Fraser University
Venue:
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part I
Year:
2010

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Abstract

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. Furthermore, 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 multifiber reconstruction methods.