Nilpotent Approximations of Sub-Riemannian Distances for Fast Perceptual Grouping of Blood Vessels in 2D and 3D

We propose an efficient approach for the grouping of local orientations (points on vessels) via nilpotent approximations of sub-Riemannian distances in the 2D and 3D roto-translation groups $SE(2)$ and $SE(3)$. In our distance approximations we consider homogeneous norms on nilpotent groups that locally approximate $SE(n)$, and which are obtained via the exponential and logarithmic map on $SE(n)$. In a qualitative validation we show that the norms provide accurate approximations of the true sub-Riemannian distances, and we discuss their relations to the fundamental solution of the sub-Laplacian on $SE(n)$. The quantitative experiments further confirm the accuracy of the approximations. Quantitative results are obtained by evaluating perceptual grouping performance of retinal blood vessels in 2D images and curves in challenging 3D synthetic volumes. The results show that 1) sub-Riemannian geometry is essential in achieving top performance and 2) that grouping via the fast analytic approximations performs almost equally, or better, than data-adaptive fast marching approaches on $\mathbb{R}^n$ and $SE(n)$.Comment: 18 pages, 9 figures, 3 tables, in review at JMI

A PDE Approach to Data-driven Sub-Riemannian Geodesics in SE(2)

We present a new flexible wavefront propagation algorithm for the boundary value problem for sub-Riemannian (SR) geodesics in the roto-translation group $SE(2) = \mathbb{R}^2 \rtimes S^1$ with a metric tensor depending on a smooth external cost $\mathcal{C}:SE(2) \to [\delta,1]$, $\delta>0$, computed from image data. The method consists of a first step where a SR-distance map is computed as a viscosity solution of a Hamilton-Jacobi-Bellman (HJB) system derived via Pontryagin's Maximum Principle (PMP). Subsequent backward integration, again relying on PMP, gives the SR-geodesics. For $\mathcal{C}=1$ we show that our method produces the global minimizers. Comparison with exact solutions shows a remarkable accuracy of the SR-spheres and the SR-geodesics. We present numerical computations of Maxwell points and cusp points, which we again verify for the uniform cost case $\mathcal{C}=1$. Regarding image analysis applications, tracking of elongated structures in retinal and synthetic images show that our line tracking generically deals with crossings. We show the benefits of including the sub-Riemannian geometry.Comment: Extended version of SSVM 2015 conference article "Data-driven Sub-Riemannian Geodesics in SE(2)

The effect of strategic patenting on cumulative innovation in UMTS standardization

Since the 1990s, intellectual property rights have become increasingly important in the telecommunications sector. In particular, the strategic role of patents played in the GSM standard irrevocably changed the IPR strategies within the sector, increasing both the revenues and barriers provided by telecom patents. The issues raised by GSM foreshadowed comparable impacts of patents upon other ICT standards. These developments parallels broader concerns raised by researchers about the risk that such patents impede the process of cumulative innovation, a problem some have labeled "the tragedy of the anticommons." After reviewing research on the various controversies regarding patents, cumulative innovation and standardization, we review the evolution of the role of patents in telecommunications standards. We then analyze the role of 1227 unique "essential" patents declared in the standardization of Universal Mobile Telecommunications System (UMTS), the thirdgeneration successor to GSM. Using a combination of data sources, we show how differences in the timing, nature and scope of patenting activities relate to firms’ business models, competitive position and role in the standardization activity. From this, we offer broader observations about the limits of existing IPR policies and coordination mechanisms, as well as the likely impact of various policy alternatives on patent proliferation in telecommunications standardization

Vesselness via multiple scale orientation scores

The multi-scale Frangi vesselness filter is an established tool in (retinal) vascular imaging. However, it cannot cope with crossings or bifurcations, since it only looks for elongated structures. Therefore, we disentangle crossing structures in the image via (multiple scale) invertible orientation scores. The described vesselness filter via scale-orientation scores performs considerably better at enhancing vessels throughout crossings and bifurcations than the Frangi version. Both methods are evaluated on a public dataset. Performance is measured by comparing ground truth data to the segmentation results obtained by basic thresholding and morphological component analysis of the filtered images

Regular SE(3) Group Convolutions for Volumetric Medical Image Analysis

Regular group convolutional neural networks (G-CNNs) have been shown to increase model performance and improve equivariance to different geometrical symmetries. This work addresses the problem of SE(3), i.e., roto-translation equivariance, on volumetric data. Volumetric image data is prevalent in many medical settings. Motivated by the recent work on separable group convolutions, we devise a SE(3) group convolution kernel separated into a continuous SO(3) (rotation) kernel and a spatial kernel. We approximate equivariance to the continuous setting by sampling uniform SO(3) grids. Our continuous SO(3) kernel is parameterized via RBF interpolation on similarly uniform grids. We demonstrate the advantages of our approach in volumetric medical image analysis. Our SE(3) equivariant models consistently outperform CNNs and regular discrete G-CNNs on challenging medical classification tasks and show significantly improved generalization capabilities. Our approach achieves up to a 16.5% gain in accuracy over regular CNNs.Comment: 10 pages, 1 figure, 2 tables, accepted at MICCAI 2023. Updated version to camera ready version

Where to go in the near future: diverging perspectives on online public service delivery

Although the electronic government is under heavy development, a clear vision doesn’t seem to exist. In this study 20 interviews among leaders in the field of e-government in the Netherlands resulted in different perspectives on the future of electronic public service delivery. The interviews revealed different objectives and interpretations of the presuppositions regarding citizens’ desires. Opinions about channel approaches and ‘trigger services’ appeared to vary. Furthermore, the respondents didn’t agree on the number of contact moments between citizen and government, had different opinions about digital skills, pled for various designs of the electronic government and placed the responsibility for electronic service delivery in different hands. Conclusion is that there is a lack of concepts on how to do things. Everybody talks about eGovernment, but all have different interpretations. \u

Diversity in knowledge transfer usage : a relational approach

In recent years, considerable attention has been paid to the effectiveness of knowledge transfer processes between academia and industry. Although there is growing evidence that the characteristics of individual researchers are important when explaining cases of successful transfer, few studies have taken the individual researcher as their unit of analysis. This study aims to use social network theory techniques to gain a better insight into knowledge transfer processes. In particular, we study how the characteristics of ties among individuals, and the interdisciplinary and pervasiveness of research affects the diversity of knowledge transfer activities. To this end, we conduct an empirical study among researchers in the field of nanotechnology. This sector is chosen for its interdisciplinarity and its expected pervasiveness. Data was collected using a survey conducted in Spain and in The Netherlands, allowing us to correct for some environmental and context effects

On genuine invariance learning without weight-tying

In this paper, we investigate properties and limitations of invariance learned by neural networks from the data compared to the genuine invariance achieved through invariant weight-tying. To do so, we adopt a group theoretical perspective and analyze invariance learning in neural networks without weight-tying constraints. We demonstrate that even when a network learns to correctly classify samples on a group orbit, the underlying decision-making in such a model does not attain genuine invariance. Instead, learned invariance is strongly conditioned on the input data, rendering it unreliable if the input distribution shifts. We next demonstrate how to guide invariance learning toward genuine invariance by regularizing the invariance of a model at the training. To this end, we propose several metrics to quantify learned invariance: (i) predictive distribution invariance, (ii) logit invariance, and (iii) saliency invariance similarity. We show that the invariance learned with the invariance error regularization closely reassembles the genuine invariance of weight-tying models and reliably holds even under a severe input distribution shift. Closer analysis of the learned invariance also reveals the spectral decay phenomenon, when a network chooses to achieve the invariance to a specific transformation group by reducing the sensitivity to any input perturbation