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 \mathbbR3 \rtimes S2Unknown control sequence '\rtimes' 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 \mathbbR3\rtimes S2Unknown control sequence '\rtimes'. 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.
|Title of host publication||Scale Space and Variational Methods in Computer Vision (Third International Conference, SSVM 2011, Ein-Gedi, Israel, May 29-June 2, 2011. Revised Selected Papers)|
|Editors||A.M. Bruckstein, B.M. Haar Romeny, ter, A.M. Bronstein, M.M. Bronstein|
|Place of Publication||Berlin|
|Publication status||Published - 2012|
|Name||Lecture Notes in Computer Science|