DCReg: Decoupled Characterization for Efficient Degenerate LiDAR Registration
Authors: Xiangcheng Hu, Xieyuanli Chen, Mingkai Jia, Jin Wu, Ping Tan, Steven L. Waslander
Abstract
LiDAR point cloud registration is fundamental to robotic perception and navigation. In geometrically degenerate environments (e.g., corridors), registration becomes ill-conditioned: certain motion directions are weakly constrained, causing unstable solutions and degraded accuracy. Existing detect-then-mitigate methods fail to reliably detect, physically interpret, and stabilize this ill-conditioning without corrupting the optimization. We introduce DCReg (Decoupled Characterization for Ill-conditioned Registration), establishing a detect-characterize-mitigate paradigm that systematically addresses ill-conditioned registration via three innovations. First, DCReg achieves reliable ill-conditioning detection by employing Schur complement decomposition on the Hessian matrix. This decouples the 6-DoF registration into 3-DoF clean rotational and translational subspaces, eliminating coupling effects that mask degeneracy in full-Hessian analyses. Second, within these subspaces, we develop interpretable characterization techniques resolving eigen-basis ambiguities via basis alignment. This establishes stable mappings between eigenspaces and physical motion directions, providing actionable insights on which motions lack constraints and to what extent. Third, leveraging this spectral information, we design a targeted mitigation via a structured preconditioner. Guided by MAP regularization, we implement eigenvalue clamping exclusively within the preconditioner rather than modifying the original problem. This preserves the least-squares objective and minimizer, enabling efficient optimization via Preconditioned Conjugate Gradient with a single interpretable parameter. Experiments demonstrate DCReg achieves 20-50% higher long-duration localization accuracy and 5-30x speedups (up to 116x) over degeneracy-aware baselines across diverse environments. Code: https://github.com/JokerJohn/DCReg
In this paper, we study 3D LiDAR scan alignment in challenging scenarios with degeneracies, such as straight corridors or flat fields, where the alignment solution is not unique and compromises localization and mapping accuracy. Existing degeneracy detection methods that neglect the potential for reassociating data points are prone to being sensitive to noise and complex degeneracies. Therefore, we propose LiLi - a novel method that leverages Lie theory to identify the full set of degenerate transformations within the SE(3) Lie group of rigid transformations. The method employs perturbations of the optimized solution and compares the resulting optimized poses to ensure robust detection of degeneracies. By leveraging generators from the Lie algebra se(3), the method provides a systematic approach to describing the set of degenerate transformations. Quantitative evaluations on synthetic data show significant improvement over the state-of-the-art Hessian-based method, reducing alignment error by 50%, with more significant improvements for datasets featuring noise. In the real-world degenerate datasets, the proposed method integrated into LiDAR-based odometry yields superior localization performance compared to the reference solution based on the Hessian-based degeneracy detector on a 260 m long trajectory, and succeeds on a 430 m long round-trip tunnel trajectory where the reference fails.
In this paper we tackle the problem of aligning LiDAR point clouds also known as the point cloud registration problem. We propose a new algorithm, PESTO, that exploits tetrahedra as "universal features" for LiDAR data, i.e., features that are agnostic to the environment where the LiDAR sensors are deployed. We show empirically that PESTO is competitive with existing solutions for aligning LiDAR point clouds, especially in environments with occlusions. Moreover, we establish PESTO's formal correctness by proving worst-case bounds on the alignment error.
Unsupervised registration of large-scale LiDAR point clouds remains challenging due to the geometric ambiguity inherent in outdoor scenes, which degrades pseudo-label quality and leads to suboptimal convergence, particularly for sparse, low-resolution scans such as those from nuScenes. We reveal that registration models intrinsically encode semantic awareness that strongly correlates with registration accuracy, albeit without explicit semantic supervision. However, this native awareness is fragile: noisy supervision arising from geometric ambiguity in unsupervised settings rapidly erodes the learned semantic structure, causing performance collapse. To this end, we propose CAESAR, a teacher-student framework guided by an off-the-shelf 3D segmentation model exclusively during training. We observe that potential inlier matches are often buried just beneath a few spurious neighbors in the noisy feature space, motivating Dual-Cue Guided Re-Matching to recover them through reselection rather than simply rejecting. Building on this, a train-only Semantic-Geometric Label Mining performs lightweight, batch-specific teacher refinement and mines reliable pseudo-labels under semantic guidance. We further introduce Semantic Predictive Distillation to consolidate the student's semantic awareness in the feature space. Extensive experiments on KITTI and nuScenes demonstrate state-of-the-art performance, with pronounced gains on the challenging nuScenes benchmark. Crucially, CAESAR incurs zero inference overhead and requires no semantic annotations on the registration data. Code will be released.