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, mismatches, and extreme 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. In this work, we revisit a 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 (SDR) 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 challenging cases with high noise levels and many outliers.