spatial projection Γ SE(2)(·) = (X (·), Y (·)) of the geodesic γ SE(2)(·) and the planar projection Γ SO(3)(·) = Π (x (·), y(·)) of the geodesic γ SO(3)(·). R. Duits received his M.Sc. degree (cum laude
We consider the problem P c u r v e of minimizing \(\int \limits _{0}^{L} \sqrt {\xi ^{2} + \kappa ^{2}(s)} \, \mathrm {d}s\) for a curve x in \(\mathbb {R}^{3}\) with fixed boundary points and directions. Here, the total length L≥0 is free, s denotes the arclength parameter, κ denotes the absolute curvature of x, and ξ>0 is constant. We lift problem P c u r v e on \(\mathbb ...
. Roto-translation group; Gauge frames; Exponential curves; Non-linear diffusion; Left-invariant image processing; Orientation scores - R. Duits and M. H. J. Janssen are joint main authors. 1
We propose two strategies to improve the quality of tractography results computed from diffusion weighted magnetic resonance imaging (DW-MRI) data. Both methods are based on the same PDE framework, defined in the coupled space of positions and orientations, associated with a stochastic process describing the enhancement of elongated structures while preserving crossing structures. ...
slope equals z0z0 . 1|z0|2 R. Duits received his M.Sc. degree (cum laude) in Mathematics in 2001 at the TU/e, The Netherlands. He received his PhD-degree (cum laude) at the Department of Biomedical
Kernels of the so-called α-scale space have the undesirable property of having no closed-form representation in the spatial domain, despite their simple closed-form expression in the Fourier domain. This obstructs spatial convolution or recursive implementation. For this reason an approximation of the 2D α-kernel in the spatial domain is presented using the well-known Gaussian ...
Inspired by the visual system of many mammals, we consider the construction of—and reconstruction from—an orientation score of an image, via a wavelet transform corresponding to the left-regular representation of the Euclidean motion group in \(\mathbb{L}_2 \)(ℝ2) and oriented wavelet φ ∈ \(\mathbb{L}_2 \)(ℝ2). Because this representation is reducible, the general wavelet ...