Numerical schemes for linear and non-linear enhancement of DW-MRI

Authors:
Eric J. Creusen;Remco Duits;Tom C. J. Dela Haije
Affiliations:
Department of Mathematics and Computer Science, Eindhoven University of Technology, The Netherlands;Department of Mathematics and Computer Science, Eindhoven University of Technology, The Netherlands;Department of Biomedical Engineering, Eindhoven University of Technology, The Netherlands
Venue:
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Year:
2011

Citing 4
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Fiber enhancement in diffusion-weighted MRI

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Abstract

We consider left-invariant diffusion processes on DTI data by embedding the data into the space $\mathbb{R}^3\rtimes S^2$ of 3D positions and orientations. We then define and solve the diffusion equation in a moving frame of reference defined using left-invariant derivatives. The diffusion process is made adaptive to the data in order to do Perona-Malik-like edge preserving smoothing, which is necessary to handle fiber structures near regions of large isotropic diffusion such as the ventricles of the brain. The corresponding partial differential systems are solved using finite difference stencils. We include experiments both on synthetic data and on DTI-images of the brain.