通过球极投影加速鲁棒于离群点的旋转估计
Accelerating Outlier-robust Rotation Estimation by Stereographic Projection
AI总结：
针对含大量离群点和噪声的大型输入中旋转估计的效率与鲁棒性问题，提出基于旋转轴几何约束、球极投影和空间投票的方法，可同时估计多旋转，GPU辅助下0.07秒解决10⁶点/90%离群点问题，角度误差0.01度，性能优于现有方法。
摘要：
旋转估计在许多计算机视觉和机器人任务中起着基础性作用。然而，在包含大量离群点（即不匹配点）和噪声的大型输入中高效估计旋转是一个公认的挑战。许多鲁棒旋转估计方法已被设计用于应对这一挑战。遗憾的是，现有方法由于计算时间长且存在局部最优风险，往往难以适用。本文提出一种高效且鲁棒的旋转估计方法：首先研究仅涉及旋转轴的几何约束，然后利用球极投影和空间投票技术识别旋转轴与角度，还能高效获得最优旋转估计并可同时估计多个旋转。为验证方法可行性，我们使用合成数据和真实世界数据进行对比实验。结果表明，在GPU辅助下，该方法可在0.07秒内解决大规模（10⁶个点）且严重污染（90%离群点率）的旋转估计问题，角度误差仅0.01度，在精度和效率上均优于现有方法。
英文摘要：
Rotation estimation plays a fundamental role in many computer vision and robot tasks. However, efficiently estimating rotation in large inputs containing numerous outliers (i.e., mismatches) and noise is a recognized challenge. Many robust rotation estimation methods have been designed to address this challenge. Unfortunately, existing methods are often inapplicable due to their long computation time and the risk of local optima. In this paper, we propose an efficient and robust rotation estimation method. Specifically, our method first investigates geometric constraints involving only the rotation axis. Then, it uses stereographic projection and spatial voting techniques to identify the rotation axis and angle. Furthermore, our method efficiently obtains the optimal rotation estimation and can estimate multiple rotations simultaneously. To verify the feasibility of our method, we conduct comparative experiments using both synthetic and real-world data. The results show that, with GPU assistance, our method can solve large-scale ($10^6$ points) and severely corrupted (90\% outlier rate) rotation estimation problems within 0.07 seconds, with an angular error of only 0.01 degrees, which is superior to existing methods in terms of accuracy and efficiency.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
