Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection
Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection
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DOI：
10.1109/lra.2020.2965893
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发表时间：
2020-04-01
影响因子：
5.2
通讯作者：
Carlone, Luca
中科院分区：
文献类型：
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作者：
Yang, Heng;Antonante, Pasquale;Carlone, Luca
半定规划 (SDP) 和平方和 (SOS) 松弛已经为多个机器人和计算机视觉问题带来了可证明的最佳非最小求解器。然而，大多数非最小求解器依赖于最小二乘公式，因此对于异常值来说很脆弱。虽然恢复针对异常值的稳健性的标准方法是使用稳健的成本函数，但后者通常会引入其他非凸性，从而阻止使用现有的非最小求解器。在这封信中，我们通过提供稳健全局估计的通用方法，实现了非最小求解器和稳健估计的同时使用，该方法可应用于非最小求解器可用于无异常值情况的任何问题。为此，我们利用稳健估计和离群值过程之间的 Black-Rangarajan 对偶性（传统上应用于早期视觉问题），并表明分级非凸性 (GNC) 可以与非最小求解器结合使用来计算稳健的解决方案，而不需要初始猜测。我们在应用中展示了由此产生的稳健的非最小求解器，包括点云和网格配准、位姿图优化和基于图像的对象位姿估计（也称为形状对齐）。我们的求解器对 70-80% 的异常值具有鲁棒性，优于 RANSAC，比专门的局部求解器更准确，并且比专门的全局求解器更快。我们还提出了第一个可证明最佳的非最小求解器，用于使用 SOS 松弛进行形状对齐。
Semidefinite Programming (SDP) and Sums-of-Squares (SOS) relaxations have led to certifiably optimal non-minimal solvers for several robotics and computer vision problems. However, most non-minimal solvers rely on least squares formulations, and, as a result, are brittle against outliers. While a standard approach to regain robustness against outliers is to use robust cost functions, the latter typically introduce other non-convexities, preventing the use of existing non-minimal solvers. In this letter, we enable the simultaneous use of non-minimal solvers and robust estimation by providing a general-purpose approach for robust global estimation, which can be applied to any problem where a non-minimal solver is available for the outlier-free case. To this end, we leverage the Black-Rangarajan duality between robust estimation and outlier processes (which has been traditionally applied to early vision problems), and show that graduated non-convexity (GNC) can be used in conjunction with non-minimal solvers to compute robust solutions, without requiring an initial guess. we demonstrate the resulting robust non-minimal solvers in applications, including point cloud and mesh registration, pose graph optimization, and image-based object pose estimation (also called shape alignment). Our solvers are robust to 70-80% of outliers, outperform RANSAC, are more accurate than specialized local solvers, and faster than specialized global solvers. We also propose the first certifiably optimal non-minimal solver for shape alignment using SOS relaxation.