28,976 research outputs found

    Self-Attention Dense Depth Estimation Network for Unrectified Video Sequences

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    The dense depth estimation of a 3D scene has numerous applications, mainly in robotics and surveillance. LiDAR and radar sensors are the hardware solution for real-time depth estimation, but these sensors produce sparse depth maps and are sometimes unreliable. In recent years research aimed at tackling depth estimation using single 2D image has received a lot of attention. The deep learning based self-supervised depth estimation methods from the rectified stereo and monocular video frames have shown promising results. We propose a self-attention based depth and ego-motion network for unrectified images. We also introduce non-differentiable distortion of the camera into the training pipeline. Our approach performs competitively when compared to other established approaches that used rectified images for depth estimation

    The Galois group of a stable homotopy theory

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    To a "stable homotopy theory" (a presentable, symmetric monoidal stable ∞\infty-category), we naturally associate a category of finite \'etale algebra objects and, using Grothendieck's categorical machine, a profinite group that we call the Galois group. We then calculate the Galois groups in several examples. For instance, we show that the Galois group of the periodic E∞\mathbf{E}_\infty-algebra of topological modular forms is trivial and that the Galois group of K(n)K(n)-local stable homotopy theory is an extended version of the Morava stabilizer group. We also describe the Galois group of the stable module category of a finite group. A fundamental idea throughout is the purely categorical notion of a "descendable" algebra object and an associated analog of faithfully flat descent in this context.Comment: 93 pages. To appear in Advances in Mathematic
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