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 (
106 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.