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Design and Processing of Invertible Orientation Scores of 3D Images

-disciplinary projects acting as a liaison between clinicians, image processing and visualization scientists and engineering teams. R. Duits received his M.Sc. degree (cum laude) in Mathematics in 2001 at the TU ... Variational Methods in Computer Vision , pp. 300 - 312 . Springer, Berlin ( 2007 ) 27. Duits , R. , Duits , M., van Almsick , M. , ter Haar Romeny, B.M.: Invertible orientation scores as an application of

Tracking of Lines in Spherical Images via Sub-Riemannian Geodesics in \({\text {SO(3)}}\)

In order to detect salient lines in spherical images, we consider the problem of minimizing the functional \(\int \limits _0^l \mathfrak {C}(\gamma (s)) \sqrt{\xi ^2 + k_g^2(s)} \, \mathrm{d}s\) for a curve \(\gamma \) on a sphere with fixed boundary points and directions. The total length l is free, s denotes the spherical arclength, and \(k_g\) denotes the geodesic curvature of...

On Sub-Riemannian Geodesics in SE(3) Whose Spatial Projections do not Have Cusps

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 {R...

Locally Adaptive Frames in the Roto-Translation Group and Their Applications in Medical Imaging

. 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

Improving Fiber Alignment in HARDI by Combining Contextual PDE Flow with Constrained Spherical Deconvolution

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...

Association Fields via Cuspless Sub-Riemannian Geodesics in SE(2)

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

ScaleSpaceViz: α-Scale spaces in practice

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...

Invertible orientation scores as an application of generalized wavelet theory

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...