Abstract
Diffusion-Weighted MRI (DW-MRI) measures local water diffusion in biological tissue, which reflects the underlying fiber structure. In order to enhance the fiber structure in the DW-MRI data we consider both (convection-)diffusions and Hamilton-Jacobi equations (erosions) on the space \(\mathbb{R}^3 \rtimes S^2\) of 3D-positions and orientations, embedded as a quotient in the group SE(3) of 3D-rigid body movements. These left-invariant evolutions are expressed in the frame of left-invariant vector fields on SE(3), which serves as a moving frame of reference attached to fiber fragments. The linear (convection-)diffusions are solved by a convolution with the corresponding Green’s function, whereas the Hamilton-Jacobi equations are solved by a morphological convolution with the corresponding Green’s function. Furthermore, we combine dilation and diffusion in pseudo-linear scale spaces on \(\mathbb{R}^{3}\rtimes S^2\). All methods are tested on DTI-images of the brain. These experiments indicate that our techniques are useful to deal with both the problem of limited angular resolution of DTI and the problem of spurious, non-aligned crossings in HARDI.
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Duits, R., Dela Haije, T.C.J., Ghosh, A., Creusen, E., Vilanova, A., ter Haar Romeny, B. (2012). Fiber Enhancement in Diffusion-Weighted MRI. In: Bruckstein, A.M., ter Haar Romeny, B.M., Bronstein, A.M., Bronstein, M.M. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2011. Lecture Notes in Computer Science, vol 6667. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24785-9_1
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DOI: https://doi.org/10.1007/978-3-642-24785-9_1
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