New Exact and Numerical Solutions of the (Convection-)Diffusion Kernels on SE(3)

Autor: Portegies, J. M., Duits, R.

We consider hypo-elliptic diffusion and convection-diffusion on $\mathbb{R}^3 \rtimes S^2$, the quotient of the Lie group of rigid body motions SE(3) in which group elements are equivalent if they are equal up to a rotation around the reference axis.

Externí odkaz: http://arxiv.org/abs/1604.03843

New Approximation of a Scale Space Kernel on SE(3) and Applications in Neuroimaging

Autor: Portegies, J. M., Sanguinetti, G. R., Meesters, S. P. L, Duits, R.

We provide a new, analytic kernel for scale space filtering of dMRI data. The kernel is an approximation for the Green's function of a hypo-elliptic diffusion on the 3D rigid body motion group SE(3), for fiber enhancement in dMRI. The enhancements ar

Externí odkaz: http://arxiv.org/abs/1506.02529

Equivariant Deep Learning via Morphological and Linear Scale Space PDEs on the Space of Positions and Orientations

Autor: Duits, R., Smets, B., Bekkers, E., Portegies, J., Elmoataz, A., Fadili, J., Quéau, Y., Rabin, J., Simon, L.

Publikováno v: Lecture Notes in Computer Science ISBN: 9783030755485
SSVM
Scale Space and Variational Methods in Computer Vision: 8th International Conference, SSVM 2021, Virtual Event, May 16–20, 2021 : proceedings, 27-39
STARTPAGE=27;ENDPAGE=39;TITLE=Scale Space and Variational Methods in Computer Vision

We present PDE-based Group Convolutional Neural Networks (PDE-G-CNNs) that generalize Group equivariant Convolutional Neural Networks (G-CNNs). In PDE-G-CNNs a network layer is a set of PDE-solvers where geometrically meaningful PDE-coefficients beco

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::249b3b95260fa7a204f38c988554bc7a
https://doi.org/10.1007/978-3-030-75549-2_3

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Brain Connectivity Measures via Direct Sub-Finslerian Front Propagation on the 5D Sphere Bundle of Positions and Directions

Autor: Portegies, J., Meesters, S., Ossenblok, P., Fuster, A., Florack, L., Duits, R., Bonet-Carne, Elisenda, Grussu, Francesco, Ning, Lipeng, Sepehrband, Farshid, Tax, Chantal M.W.

Publikováno v: Computational Diffusion MRI ISBN: 9783030058302
Computational Diffusion MRI: International MICCAI Workshop, Granada, Spain, September 2018, 309-321
STARTPAGE=309;ENDPAGE=321;TITLE=Computational Diffusion MRI
Computational diffusion MRI: International MICCAI Workshop, Granada, Spain, September 2018, 309-321
STARTPAGE=309;ENDPAGE=321;TITLE=Computational diffusion MRI

We propose a novel connectivity measure between brain regions using diffusion-weighted MRI. This connectivity measure is based on optimal sub-Finslerian geodesic front propagation on the 5D base manifold of (3D) positions and (2D) directions, the so-

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::43fca38f74df2c7b7162ec67b6bb47f7
https://cris.maastrichtuniversity.nl/en/publications/cb99a538-1567-4819-ae1c-e7a4de1655e9