The Iterative Closest Point (ICP) algorithm and its variants are a
fundamental technique for rigid registration between two point sets, with wide
applications in different areas from robotics to 3D reconstruction. The main
drawbacks for ICP are its slow convergence as well as its sensitivity to
outliers, missing data, and partial overlaps. Recent work such as Sparse ICP
achieves robustness via sparsity optimization at the cost of computational
speed. In this paper, we propose a new method for robust registration with fast
convergence. First, we show that the classical point-to-point ICP can be
treated as a majorization-minimization (MM) algorithm, and propose an Anderson
acceleration approach to speed up its convergence. In addition, we introduce a
robust error metric based on the Welsch's function, which is minimized
efficiently using the MM algorithm with Anderson acceleration. On challenging
datasets with noises and partial overlaps, we achieve similar or better
accuracy than Sparse ICP while being at least an order of magnitude faster.
Finally, we extend the robust formulation to point-to-plane ICP, and solve the
resulting problem using a similar Anderson-accelerated MM strategy. Our robust
ICP methods improve the registration accuracy on benchmark datasets while being
competitive in computational time.

本文提出了一种快速并具有鲁棒性的 Iterative Closest Point 方法，通过将点对点 ICP 视为主性 - 最小化算法，并采用 Anderson 加速方法加速其收敛速度并引入基于 Welsch 函数的鲁棒误差度量。在具有噪声和部分重叠的数据集上，我们实现了与稀疏 ICP 相似或更好的准确性，而速度至少快一个数量级。最后，我们将鲁棒的形式扩展到了点对平面 ICP，并使用类似的 Anderson 加速 MM 策略解决了相应的问题。