Eigenvalues of a real supersymmetric tensor
Journal of Symbolic Computation
Neural Tractography Using an Unscented Kalman Filter
IPMI '09 Proceedings of the 21st International Conference on Information Processing in Medical Imaging
ODF maxima extraction in spherical harmonic representation via analytical search space reduction
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part II
Symmetric positive-definite cartesian tensor orientation distribution functions (CT-ODF)
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part I
Higher Order Positive Semidefinite Diffusion Tensor Imaging
SIAM Journal on Imaging Sciences
Detection of crossing white matter fibers with high-order tensors and rank-k decompositions
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
A polynomial approach for maxima extraction and its application to tractography in HARDI
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Probabilistic tractography using Q-ball modeling and particle filtering
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Approximating Symmetric Positive Semidefinite Tensors of Even Order
SIAM Journal on Imaging Sciences
Nonnegative Diffusion Orientation Distribution Function
Journal of Mathematical Imaging and Vision
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In this work, a novel method for determining the principal directions (maxima) of the diffusion orientation distribution function(ODF) is proposed. We represent the ODF as a symmetric high-order Cartesian tensor restricted to the unit sphere and show that the extrema of the ODF are solutions to a system of polynomial equations whose coefficients are polynomial functions of the tensor elements. In addition to demonstrating the ability of our methods to identify the principal directions in real data, we show that this method correctly identifies the principal directions under a range of noise levels. We also propose the use of the principal curvatures of the graph of the ODF function as a measure of the degree of diffusion anisotropy in that direction. We present simulated results illustrating the relationship between the mean principal curvature, measured at the maxima, and the fractional anisotropy of the underlying diffusion tensor.