Deep Learning for Vanishing Point Detection Using an Inverse Gnomonic Projection

We present a novel approach for vanishing point detection from uncalibrated monocular images. In contrast to state-of-the-art, we make no a priori assumptions about the observed scene. Our method is based on a convolutional neural network (CNN) which does not use natural images, but a Gaussian sphere representation arising from an inverse gnomonic projection of lines detected in an image. This allows us to rely on synthetic data for training, eliminating the need for labelled images. Our method achieves competitive performance on three horizon estimation benchmark datasets. We further highlight some additional use cases for which our vanishing point detection algorithm can be used.Comment: Accepted for publication at German Conference on Pattern Recognition (GCPR) 2017. This research was supported by German Research Foundation DFG within Priority Research Programme 1894 "Volunteered Geographic Information: Interpretation, Visualisation and Social Computing

Adaptive computation of gravitational waves from black hole interactions

We construct a class of linear partial differential equations describing general perturbations of non-rotating black holes in 3D Cartesian coordinates. In contrast to the usual approach, a single equation treats all radiative $\ell -m$ modes simultaneously, allowing the study of wave perturbations of black holes with arbitrary 3D structure, as would be present when studying the full set of nonlinear Einstein equations describing a perturbed black hole. This class of equations forms an excellent testbed to explore the computational issues of simulating black spacetimes using a three dimensional adaptive mesh refinement code. Using this code, we present results from the first fully resolved 3D solution of the equations describing perturbed black holes. We discuss both fixed and adaptive mesh refinement, refinement criteria, and the computational savings provided by adaptive techniques in 3D for such model problems of distorted black holes.Comment: 16 Pages, RevTeX, 13 figure

Hinge-Wasserstein: Mitigating Overconfidence in Regression by Classification

Modern deep neural networks are prone to being overconfident despite their drastically improved performance. In ambiguous or even unpredictable real-world scenarios, this overconfidence can pose a major risk to the safety of applications. For regression tasks, the regression-by-classification approach has the potential to alleviate these ambiguities by instead predicting a discrete probability density over the desired output. However, a density estimator still tends to be overconfident when trained with the common NLL loss. To mitigate the overconfidence problem, we propose a loss function, hinge-Wasserstein, based on the Wasserstein Distance. This loss significantly improves the quality of both aleatoric and epistemic uncertainty, compared to previous work. We demonstrate the capabilities of the new loss on a synthetic dataset, where both types of uncertainty are controlled separately. Moreover, as a demonstration for real-world scenarios, we evaluate our approach on the benchmark dataset Horizon Lines in the Wild. On this benchmark, using the hinge-Wasserstein loss reduces the Area Under Sparsification Error (AUSE) for horizon parameters slope and offset, by 30.47% and 65.00%, respectively

Trace-gas metabolic versatility of the facultative methanotroph Methylocella silvestris

The climate-active gas methane is generated both by biological processes and by thermogenic decomposition of fossil organic material, which forms methane and short-chain alkanes, principally ethane, propane and butane1, 2. In addition to natural sources, environments are exposed to anthropogenic inputs of all these gases from oil and gas extraction and distribution. The gases provide carbon and/or energy for a diverse range of microorganisms that can metabolize them in both anoxic3 and oxic zones. Aerobic methanotrophs, which can assimilate methane, have been considered to be entirely distinct from utilizers of short-chain alkanes, and studies of environments exposed to mixtures of methane and multi-carbon alkanes have assumed that disparate groups of microorganisms are responsible for the metabolism of these gases. Here we describe the mechanism by which a single bacterial strain, Methylocella silvestris, can use methane or propane as a carbon and energy source, documenting a methanotroph that can utilize a short-chain alkane as an alternative to methane. Furthermore, during growth on a mixture of these gases, efficient consumption of both gases occurred at the same time. Two soluble di-iron centre monooxygenase (SDIMO) gene clusters were identified and were found to be differentially expressed during bacterial growth on these gases, although both were required for efficient propane utilization. This report of a methanotroph expressing an additional SDIMO that seems to be uniquely involved in short-chain alkane metabolism suggests that such metabolic flexibility may be important in many environments where methane and short-chain alkanes co-occur

Adaptive mesh and geodesically sliced Schwarzschild spacetime in 3+1 dimensions

We present first results obtained with a 3+1 dimensional adaptive mesh code in numerical general relativity. The adaptive mesh is used in conjunction with a standard ADM code for the evolution of a dynamically sliced Schwarzschild spacetime (geodesic slicing). We argue that adaptive mesh is particularly natural in the context of general relativity, where apart from adaptive mesh refinement for numerical efficiency one may want to use the built in flexibility to do numerical relativity on coordinate patches.Comment: 21 pages, LaTeX, 7 figures included with eps

Surface Geometry of 5D Black Holes and Black Rings

We discuss geometrical properties of the horizon surface of five-dimensional rotating black holes and black rings. Geometrical invariants characterizing these 3D geometries are calculated. We obtain a global embedding of the 5D rotating black horizon surface into a flat space. We also describe the Kaluza-Klein reduction of the black ring solution (along the direction of its rotation) which relates this solution to the 4D metric of a static black hole distorted by the presence of external scalar (dilaton) and vector (`electromagnetic') field. The properties of the reduced black hole horizon and its embedding in \E^3 are briefly discussed.Comment: 10 pages, 9 figures, Revtex