Directional functions for orientation distribution estimation

Y. Rathi, O. Michailovich, M. E. Shenton, S. Bouix
Med Image Anal
2009

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Abstract

Computing the orientation distribution function (ODF) from high angular resolution diffusion imaging (HARDI) signals makes it possible to determine the orientation of fiber bundles of the brain. The HARDI signals are samples measured from a spherical shell and thus require processing on the sphere. Past work on ODF estimation involved using the spherical harmonics or spherical radial basis functions. In this work, we propose three novel directional functions able to represent the measured signals in a very compact manner, i.e., they require very few parameters to completely describe the measured signal. Analytical expressions are derived for computing the corresponding ODF. The directional functions can represent diffusion in a particular direction and mixture models can be used to represent multi-fiber orientations. We show how to estimate the parameters of this mixture model and elaborate on the differences between these functions. We also compare this general framework with estimation of ODF using spherical harmonics on some real and synthetic data. The proposed method could be particularly useful in applications such as tractography and segmentation. Details are also given on different ways in which interpolation can be performed using directional functions. In particular, we discuss a complete Euclidean as well as a "hybrid" framework, comprising of the Riemannian as well as Euclidean spaces, to perform interpolation and compute geodesic distances between two ODF's.


Reference

Rathi Y, Michailovich O, Shenton ME, Bouix S. Directional functions for orientation distribution estimation. Med Image Anal 2009;.

Grants

NIH P41 RR13218, K05 MH 070047, 1P50 MH080272-01, R01 MH 52807, R01 MH 50740, NIH U54 GM072977-01, U54 EB005149 NIBIB NIH

Research area

dti
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