A Robust 3D Registration Method via Simultaneous Inlier Identification and Model Estimation

Robust 3D registration is a fundamental problem in computer vision and robotics, where the goal is to estimate the geometric transformation between two sets of measurements in the presence of noise and outlier contamination. Existing robust registration methods are mainly built on either maximum consensus (MC) estimators, which first identify inliers and then estimate the transformation, or M-estimators, which directly optimize a robust objective. However, MC-based methods typically ignore residual magnitudes during inlier selection, while many M-estimators do not explicitly couple inlier/outlier identification with model estimation. Thus, a unified and efficient framework that jointly performs inlier identification and accurate transformation estimation remains desirable for challenging 3D registration. In this work, we introduce a unified truncated-loss based formulation for simultaneous inlier identification and model estimation (SIME) and study it in the context of 3D registration. We show that, compared with MC-based robust fitting, SIME can achieve a lower fitting residual because it incorporates residual magnitudes into the inlier selection process. To solve the resulting nonconvex problem, we develop an alternating minimization (AM) algorithm, and further propose an AM method embedded with semidefinite relaxation (AM-R) to alleviate the difficulty caused by the binary inlier variables. We instantiate the proposed framework for 3D rotation search and rigid point-set registration using quaternion-based formulations. Experimental results on both simulated and real-world registration tasks demonstrate that the proposed methods compare favorably with strong baseline solvers, especially in high noise and extreme outliers. In the synthetic experiments, the proposed methods are evaluated under outlier ratios up to 95% and consistently achieve competitive or better accuracy, with clear advantages in high-noise cases. On 3DMatch, SIME (AM) achieves a mean registration success rate of 91.0%. These results show the potential of SIME for reliable 3D registration in practical robotics, computer vision, and geometric perception applications.