Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.neuroimage.2011.01.053
Title: A nonparametric Riemannian framework for processing high angular resolution diffusion images and its applications to ODF-based morphometry
Authors: Goh, A. 
Lenglet, C.
Thompson, P.M.
Vidal, R.
Keywords: Diffusion weighted MRI
High angular resolution diffusion imaging
Issue Date: 1-Jun-2011
Source: Goh, A., Lenglet, C., Thompson, P.M., Vidal, R. (2011-06-01). A nonparametric Riemannian framework for processing high angular resolution diffusion images and its applications to ODF-based morphometry. NeuroImage 56 (3) : 1181-1201. ScholarBank@NUS Repository. https://doi.org/10.1016/j.neuroimage.2011.01.053
Abstract: High angular resolution diffusion imaging (HARDI) has become an important technique for imaging complex oriented structures in the brain and other anatomical tissues. This has motivated the recent development of several methods for computing the orientation probability density function (PDF) at each voxel. However, much less work has been done on developing techniques for filtering, interpolation, averaging and principal geodesic analysis of orientation PDF fields. In this paper, we present a Riemannian framework for performing such operations. The proposed framework does not require that the orientation PDFs be represented by any fixed parameterization, such as a mixture of von Mises-Fisher distributions or a spherical harmonic expansion. Instead, we use a nonparametric representation of the orientation PDF. We exploit the fact that under the square-root re-parameterization, the space of orientation PDFs forms a Riemannian manifold: the positive orthant of the unit Hilbert sphere. We show that various orientation PDF processing operations, such as filtering, interpolation, averaging and principal geodesic analysis, may be posed as optimization problems on the Hilbert sphere, and can be solved using Riemannian gradient descent. We illustrate these concepts with numerous experiments on synthetic, phantom and real datasets. We show their application to studying left/right brain asymmetries. © 2011 Elsevier Inc.
Source Title: NeuroImage
URI: http://scholarbank.nus.edu.sg/handle/10635/102697
ISSN: 10538119
DOI: 10.1016/j.neuroimage.2011.01.053
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