用球面投影加速鲁棒旋转估计，百万点数据0.07秒完成。
Accelerating Outlier-robust Rotation Estimation by Stereographic Projection
- 通过球面投影与空间投票定位旋转轴和角度。
- 90%误匹配下仍保持0.01度误差，百万点仅需0.07秒。
- 适合大规模、高噪声场景的实时旋转估计任务。
旋转估计在计算机视觉与机器人任务中至关重要。然而，在包含大量异常值（即错误匹配）和噪声的大规模输入中高效估计旋转仍是公认难题。尽管已有多种鲁棒旋转估计方法，但其计算时间长且易陷入局部最优，实际应用受限。本文提出一种高效且鲁棒的旋转估计方法：首先分析仅涉及旋转轴的几何约束；随后利用球面投影与空间投票技术识别旋转轴与角度；进一步高效求解最优旋转，并可同时估计多个旋转。通过合成数据与真实数据的对比实验验证，结合GPU加速，本方法可在0.07秒内完成含10⁶点、90%异常值的严重污染旋转估计，角误差仅0.01度，精度与效率均优于现有方法。
原文摘要 · Abstract (English)
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.
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