PESTO: Formally Correct Registration of LiDAR Point Clouds with Limited Overlap

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

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.

Image-to-Point Cloud Registration (I2P) is essential for integrating camera and LiDAR in perception and autonomous systems, yet the modality gap between images and point clouds makes it difficult to achieve both high accuracy and strong generalization. In this paper, we propose a simple yet effective I2P method that treats LiDAR as an imaging sensor: from a single sparse LiDAR scan, we generate a dense LiDAR intensity image using Conditional Rectified Flow, match it with a camera image using a pre-trained feature matcher, and estimate the 6-DoF relative pose via PnP-RANSAC. The proposed model is pre-trained through a self-supervised image completion task and fine-tuned on a small amount of LiDAR data (neither image-point cloud pairs nor ground-truth sensor poses are required), enabling it to scale to diverse LiDAR and camera configurations. Experiments on the R3LIVE dataset show that the proposed method achieves a mean error of 4.89° / 1.63 m, outperforming existing methods, while completing a single registration in approximately 0.68 s.