A nonparametric riemannian framework for processing high angular resolution diffusion images (HARDI)

Alvina Goh, Christophe Lenglet, Paul M. Thompson, René Vidal

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

High angular resolution diffusion imaging has become an important magnetic resonance technique for in vivo imaging. Most current research in this field focuses on developing methods for computing the orientation distribution function (ODF), which is the probability distribution function of water molecule diffusion along any angle on the sphere. In this paper, we present a Riemannian framework to carry out computations on an ODF field. The proposed framework does not require that the ODFs be represented by any fixed parameterization, such as a mixture of von Mises-Fisher distributions or a spherical harmonic expansion. Instead, we use a non-parametric representation of the ODF, and exploit the fact that under the square-root re-parameterization, the space of ODFs forms a Riemannian manifold, namely the unit Hilbert sphere. Specifically, we use Riemannian operations to perform various geometric data processing algorithms, such as interpolation, convolution and linear and nonlinear filtering. We illustrate these concepts with numerical experiments on synthetic and real datasets.

Original languageEnglish (US)
Title of host publication2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009
PublisherIEEE Computer Society
Pages2496-2503
Number of pages8
Volume2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition
ISBN (Print)9781424439935
DOIs
StatePublished - Jan 1 2009
Event2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Miami, FL, United States
Duration: Jun 20 2009Jun 25 2009

Other

Other2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition
CountryUnited States
CityMiami, FL
Period6/20/096/25/09

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