A Practical $O(N^2)$O(N2) Outlier Removal Method for Correspondence-Based Point Cloud Registration

Point cloud registration (PCR) is an important and fundamental problem in 3D computer vision, whose goal is to seek an optimal rigid model to register a point cloud pair. Correspondence-based PCR techniques do not require initial guesses and gain more attentions. However, 3D keypoint techniques are much more difficult than their 2D counterparts, which results in extremely high outlier rates. Current robust techniques suffer from very high computational cost. In this paper, we propose a polynomial time ($O(N^2)$, where $N$ is the number of correspondences.) outlier removal method. Its basic idea is to reduce the input set into a smaller one with a lower outlier rate based on bound principle. To seek tight lower and upper bounds, we originally define two concepts, i.e., correspondence matrix (CM) and augmented correspondence matrix (ACM). We propose a cost function to minimize the determinant of CM or ACM, where the cost of CM rises to a tight lower bound and the cost of ACM leads to a tight upper bound. Then, we propose a scale-adaptive Cauchy estimator (SA-Cauchy) for further optimization. Extensive experiments on simulated and real PCR datasets demonstrate that the proposed method is robust at outlier rates above 99 percent and 1$\sim$2 orders faster than its competitors. The source code will be made publicly available in https://ljy-rs.github.io/web/.