We introduce apex point map, a simple data structure for constructing conservative bounds for rigid objects. The data structure is distilled from a dense k-DOP, and can be queried in constant time to determine a tight bounding plane with any given normal vector. Both precalculation and lookup can be implemented very efficiently on current GPUs. Applications include, e.g., finding tight world-space bounds for transformed meshes, determining per-object shadow map extents, more accurate view frustum culling, and collision detection.

We present a method for extreme occluder simplification. We take a triangle soup as input, and produce a small set of polygons with closely matching occlusion properties. In contrast to methods that optimize the original geometry, our algorithm has very few requirements for the input—specifically, the input does not need to be a watertight, two-manifold mesh. This robustness is achieved by working on a well-behaved, discretized representation of the input instead of the original, potentially badly structured geometry.

We propose an efficient acceleration structure for real-time screen-space ray tracing. The hybrid data structure represents the scene geometry by combining a bounding volume hierarchy with local planar approximations. This enables fast empty space skipping while tracing and yields exact intersection points for the planar approximation. In combination with an occlusion-aware ray traversal our algorithm is capable to quickly trace even multiple depth layers.

State-of-the-art methods for geometric anti-aliasing in real-time rendering are based on Multi-Sample Anti-Aliasing (MSAA), which samples visibility more than shading to reduce the number of expensive shading calculations. However, for high-quality results the number of visibility samples needs to be large (e.g., 64 samples/pixel), which requires significant memory because visibility samples are usually 24-bit depth values.

In this technical report we study different parallel graph coloring algorithms and their application to the incomplete-LU factorization. We implement graph coloring based on different heuristics and showcase their performance on the GPU. We also present a comprehensive comparison of level-scheduling and graph coloring approaches for the incomplete-LU factorization and triangular solve. We discuss their tradeoffs and differences from the mathematics and computer science prospective. Finally we present numerical experiments that showcase the performance of both algorithms.

We describe a method to compute the internal parameters (focal and principal point) of a camera with known position and orientation, based on the observation of two or more conics on a known plane. The conics can even be degenerate (e.g., pairs of lines). The proposed method can be used to re-estimate the internal parameters of a fully calibrated camera after zooming to a new, unknown, focal length. It also allows estimating the internal parameters when a second, fully calibrated camera observes the same conics.

Physically correct rendering of environment illumination has been a long-standing challenge in interactive graphics, since Monte-Carlo ray-tracing requires thousands of rays per pixel. We propose accurate filtering of a noisy Monte-Carlo image using Fourier analysis. Our novel analysis extends previous works by showing that the shape of illumination spectra is not always a line or wedge, as in previous approximations, but rather an ellipsoid.

Touchless hand gesture recognition systems are becoming important in automotive user interfaces as they improve safety and comfort. Various computer vision algorithms have employed color and depth cameras for hand gesture recognition, but robust classification of gestures from different subjects performed under widely varying lighting conditions is still challenging.

Intelligent driver assistance systems have become important in the automotive industry. One key element of such systems is a smart user interface that tracks and recognizes drivers' hand gestures. %Various computer vision systems using optical and depth sensors have been introduced for sensing (tracking/recognition) dynamic gestures. Hand gesture sensing using traditional computer vision techniques is challenging because of wide variations in lighting conditions, e.g., inside a car.

We propose a novel multi-sensor system for accurate and power-efficient dynamic car-driver hand-gesture recognition, using a short-range radar, a color camera, and a depth camera, which together make the system robust against variable lighting conditions. We present a procedure to jointly calibrate the radar and depth sensors. We employ convolutional deep neural networks to fuse data from multiple sensors and to classify the gestures. Our algorithm accurately recognizes 10 different gestures acquired indoors and outdoors in a car during the day and at night.