Plane-extraction from depth-data using a Gaussian mixture regression model

We propose a novel algorithm for unsupervised extraction of piecewise planar models from depth-data. Among other applications, such models are a good way of enabling autonomous agents (robots, cars, drones, etc.) to effectively perceive their surroundings and to navigate in three dimensions. We propose to do this by fitting the data with a piecewise-linear Gaussian mixture regression model whose components are skewed over planes, making them flat in appearance rather than being ellipsoidal, by embedding an outlier-trimming process that is formally incorporated into the proposed expectation-maximization algorithm, and by selectively fusing contiguous, coplanar components. Part of our motivation is an attempt to estimate more accurate plane-extraction by allowing each model component to make use of all available data through probabilistic clustering. The algorithm is thoroughly evaluated against a standard benchmark and is shown to rank among the best of the existing state-of-the-art methods.Comment: 11 pages, 2 figures, 1 tabl

Constraining new resonant physics with top spin polarisation information

We provide a comprehensive analysis of the power of including top quark-polarisation information to kinematically challenging $t\bar t$ resonance searches, for which ATLAS and CMS start losing sensitivity. Following the general modeling and analysis strategies pursued by the experiments, we analyse the semi-leptonic and the di-lepton $t\bar t$ channels and show that including polarisation information can lead to large improvements in the limit setting procedures with large data sets. This will allow us to set limits for parameter choices where sensitivity from $m(t\bar t)$ is not sufficient. This highlights the importance of spin observables as part of a more comprehensive set of observables to gain sensitivity to BSM resonance searches.Comment: 13 pages, 11 figure

Contact detection between a small ellipsoid and another quadric

[Abstract] We analyze the characteristic polynomial associated to an ellipsoid and another quadric in the context of the contact detection problem. We obtain a necessary and sufficient condition for an efficient method to detect contact. This condition, named smallness condition, is a feature on the size and the shape of the quadrics and can be checked directly from their parameters. Under this hypothesis, contact can be noticed by means of the expressions in a discriminant system of the characteristic polynomial. Furthermore, relative positions can be classified through the sign of the coefficients of this polynomial. As an application of these results, a method to detect contact between a small ellipsoid and a combination of quadrics is given

Complete Classification and Efficient Determination of Arrangements Formed by Two Ellipsoids

International audienceArrangements of geometric objects refer to the spatial partitions formed by the objects and they serve as an underlining structure of motion design, analysis and planning in CAD/CAM, robotics, molecular modeling, manufacturing and computer-assisted radio-surgery. Arrangements are especially useful to collision detection, which is a key task in various applications such as computer animation , virtual reality, computer games, robotics, CAD/CAM and computational physics. Ellipsoids are commonly used as bounding volumes in approximating complex geometric objects in collision detection. In this paper we present an in-depth study on the arrangements formed by two ellipsoids. Specifically, we present a classification of these arrangements and propose an efficient algorithm for determining the arrangement formed by any particular pair of ellipsoids. A stratification diagram is also established to show the connections among all the arrangements formed by two ellipsoids. Our results for the first time elucidate all possible relative positions between two arbitrary ellipsoids and provides an efficient and robust algorithm for determining the relative position of any two given ellipsoids, therefore providing the necessary foundation for developing practical and trustworthy methods for processing ellipsoids for collision analysis or simulation in various applications