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 language | English (US) |
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Title of host publication | 2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, CVPR Workshops 2009 |
Publisher | IEEE Computer Society |
Pages | 2496-2503 |
Number of pages | 8 |
Volume | 2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition |
ISBN (Print) | 9781424439935 |
DOIs | |
State | Published - Jan 1 2009 |
Event | 2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Miami, FL, United States Duration: Jun 20 2009 → Jun 25 2009 |
Other
Other | 2009 IEEE Computer Society Conference on Computer Vision and Pattern Recognition |
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Country/Territory | United States |
City | Miami, FL |
Period | 6/20/09 → 6/25/09 |