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RGB-D terrain perception and dense mapping for legged robots

Dominik Belter, Przemysław Łabecki, Péter Fankhauser, Roland Siegwart (2016)

International Journal of Applied Mathematics and Computer Science

This paper addresses the issues of unstructured terrain modeling for the purpose of navigation with legged robots. We present an improved elevation grid concept adopted to the specific requirements of a small legged robot with limited perceptual capabilities. We propose an extension of the elevation grid update mechanism by incorporating a formal treatment of the spatial uncertainty. Moreover, this paper presents uncertainty models for a structured light RGB-D sensor and a stereo vision camera used...

Robust optimality of Gaussian noise stability

Elchanan Mossel, Joe Neeman (2015)

Journal of the European Mathematical Society

We prove that under the Gaussian measure, half-spaces are uniquely the most noise stable sets. We also prove a quantitative version of uniqueness, showing that a set which is almost optimally noise stable must be close to a half-space. This extends a theorem of Borell, who proved the same result but without uniqueness, and it also answers a question of Ledoux, who asked whether it was possible to prove Borell’s theorem using a direct semigroup argument. Our quantitative uniqueness result has various...

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