Fast and Robust Iterative Closest Point
"Fast and Robust Iterative Closest Point" by Juyong Zhang, Yuxin Yao, and Bailin Deng addresses two main drawbacks of the traditional Iterative Closest Point (ICP) algorithm: its slow convergence and sensitivity to outliers, missing data, and partial overlaps. ICP is fundamental for rigid registration between two point sets, widely used in fields such as robotics and 3D reconstruction. However, recent solutions like Sparse ICP have achieved robustness at the expense of computational speed. The authors present a novel method that enhances both robustness and convergence speed.
The paper first reframes the classical ICP's point-to-point registration task as a majorization-minimization (MM) algorithm. To accelerate convergence, the authors propose using Anderson acceleration—a well-regarded numerical technique—to the MM framework of ICP, which speeds up convergence significantly compared to existing ICP variations. The approach focuses on computational efficiency without requiring high-order information like normals or curvature, which can be unreliable in noisy data.
A critical component of the new method is a robust error metric based on Welsch's function, a function that provides insensitivity to outliers and partial data overlaps. This function, when integrated into the ICP framework, improves robustness and efficiency, demonstrated through experiments that yield similar or better accuracy than Sparse ICP but at least an order of magnitude faster. The authors present compelling results on challenging datasets characterized by noise and partial overlaps, highlighting that the robust ICP formulation enhances both computational efficiency and registration accuracy.
Beyond the point-to-point ICP improvement, the paper extends these robust acceleration techniques to the point-to-plane ICP. This is a significant contribution because point-to-plane ICP is well-known for its faster convergence due to local linear approximations. Even in this context, the Anderson-accelerated MM approach shows improved performance, further attesting to the flexibility and strength of this optimization strategy.
The implications of this research extend to any application requiring robust and efficient point set registration. This has practical ramifications in areas such as 3D reconstruction from partial scans and robust robotic vision systems in unstructured environments, where data often contains missing parts and numerous outliers. The theoretical contribution lies in the combination of MM algorithms and Anderson acceleration—a less explored area in computer graphics and vision—which paves the way for future studies enhancing other types of geometric optimization problems.
The insights and techniques proposed in this paper could easily stimulate new developments in AI, particularly those involving spatial data interpretation, paving the way for creating faster and more robust registration algorithms that adapt flexibly to a broad set of scenarios. This robust ICP methodology holds potential beyond existing datasets, offering a generalized framework that could be adapted for future AI tasks with increasing spatial complexity.