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 paper, 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. Although GNC's global optimality cannot be guaranteed, we demonstrate
the empirical robustness of 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.

本研究提出了一种可应用于任何非最小化求解器的鲁棒全局估计通用方法，该方法利用了鲁棒估计与异常值处理之间的 Black-Rangarajan 对偶并结合逐步非凸性与 SDP 解法求解，解决了常规稳健代价函数导致的非凸性问题；本方法应用于点云和网格登记，位姿图优化和基于图像的形状算法中，具有 70-80％异常值鲁棒性，并且比专门的局部求解器更准确和更快。