论文标题
旨在理解在健壮旋转搜索中截短最小二乘的半决赛放松
Towards Understanding The Semidefinite Relaxations of Truncated Least-Squares in Robust Rotation Search
论文作者
论文摘要
旋转搜索问题旨在找到最能与给定数量的点对对齐的3D旋转。为了诱导对异常值进行旋转搜索的鲁棒性，先前的工作将截短的最小二乘（TLS）视为一个非凸优化问题，其半芬矿松弛（SDR）是可拖动的替代方案。在理论上，在存在噪声，异常值或两个方面，该SDR在很大程度上都没有探索。我们得出了表征该SDR紧密度的条件，表明紧密度取决于噪声水平，TLS的截断参数以及离群分布（随机或聚类）。特别是，我们简短地证明了无噪声和无离群的案例中的紧密性，而不是对先前工作的冗长分析。
The rotation search problem aims to find a 3D rotation that best aligns a given number of point pairs. To induce robustness against outliers for rotation search, prior work considers truncated least-squares (TLS), which is a non-convex optimization problem, and its semidefinite relaxation (SDR) as a tractable alternative. Whether this SDR is theoretically tight in the presence of noise, outliers, or both has remained largely unexplored. We derive conditions that characterize the tightness of this SDR, showing that the tightness depends on the noise level, the truncation parameters of TLS, and the outlier distribution (random or clustered). In particular, we give a short proof for the tightness in the noiseless and outlier-free case, as opposed to the lengthy analysis of prior work.
