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)

Emerging coordination mechanisms for multi-party IPR holders: linking research with standardization

The standards setting process relies to an increasing degree on successfully integrating up-to-date research and development results (R&D). The successful interaction between research and standards can provide important social benefits. But, to do so, a number of challenges need to be faced. One key and persistent challenge is to provide the conditions in which the cross-purposes of formal standards-setting bodies and intellectual property rights can equitably be accommodated. This means balancing the collective gains to be reaped from the elaboration of a common standard against the individual gains to be allocated to relevant individual rights-holders. This discussion paper focuses on approaches to the reemerging tension between intellectual-property-rights and standards. It points to the importance that successful approaches can have to improve the interaction the between research and standardization activities. It then goes on to consider the (re)emergence of two approaches that are indicative of the changing relationship between intellectual property rights and standards-setting bodies

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