112 citations · 411 across the 40 of their papers we have counts for
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Total Variation and Mean Curvature PDEs on
Remco Duits, Etienne St-Onge, Jim Portegies +1
Total variation regularization and total variation flows (TVF) have been widely applied for image enhancement and denoising. To include a generic preservation of crossing curviline…
Fourier Transform on the Homogeneous Space of 3D Positions and Orientations for Exact Solutions to Linear Parabolic and (Hypo-)Elliptic PDEs
Remco Duits, Erik J. Bekkers, Alexey Mashtakov
Fokker-Planck PDEs (incl. diffusions) for stable Lévy processes (incl. Wiener processes) on the joint space of positions and orientations play a major role in mechanics, robotics,…
New Approximation of a Scale Space Kernel on SE(3) and Applications in Neuroimaging
J. M. Portegies, G. R. Sanguinetti, S. P. L Meesters +1
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…
Left-invariant evolutions of wavelet transforms on the Similitude Group
U. Sharma, R. Duits
Enhancement of multiple-scale elongated structures in noisy image data is relevant for many biomedical applications but commonly used PDE-based enhancement techniques often fail at…
Evolution Equations on Gabor Transforms and their Applications
Remco Duits, Hartmut Führ, Bart Janssen +3
We introduce a systematic approach to the design, implementation and analysis of left-invariant evolution schemes acting on Gabor transform, primarily for applications in signal an…
Diffusion, Convection and Erosion on SE(3)/({0} \times SO(2)) and their Application to the Enhancement of Crossing Fibers
Remco Duits, Eric Creusen, Arpan Ghosh +1
In this article we study both left-invariant (convection-)diffusions and left-invariant Hamilton-Jacobi equations on the space SE(3)/({0} \times SO(2)) of 3D-positions and orientat…