# DCReg: Decoupled Characterization for Efficient Degenerate LiDAR Registration

arXiv: https://arxiv.org/abs/2509.06285 · HTML: https://mlsanity.com/paper/2509.06285/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 67 references that are in the map.
- First posted on arXiv 8 Sep 2025.

## Builds on (most cited first, 26 of 26)

- [Open3D: A Modern Library for 3D Data Processing](https://mlsanity.com/paper/1801.09847/) (2018)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [LIO-SAM: Tightly-coupled Lidar Inertial Odometry via Smoothing and Mapping](https://mlsanity.com/paper/2007.00258/) (2020)
- [KISS-ICP: In Defense of Point-to-Point ICP -- Simple, Accurate, and Robust Registration If Done the Right Way](https://mlsanity.com/paper/2209.15397/) (2022)
- [GeoTransformer: Fast and Robust Point Cloud Registration with Geometric Transformer](https://mlsanity.com/paper/2308.03768/) (2023)
- [Tightly Coupled 3D Lidar Inertial Odometry and Mapping](https://mlsanity.com/paper/1904.06993/) (2019)
- [RING++: Roto-translation Invariant Gram for Global Localization on a Sparse Scan Map](https://mlsanity.com/paper/2210.05984/) (2022)
- [SubT-MRS Dataset: Pushing SLAM Towards All-weather Environments](https://mlsanity.com/paper/2307.07607/) (2023)
- [X-ICP: Localizability-Aware LiDAR Registration for Robust Localization in Extreme Environments](https://mlsanity.com/paper/2211.16335/) (2022)
- [LINS: A Lidar-Inertial State Estimator for Robust and Efficient Navigation](https://mlsanity.com/paper/1907.02233/) (2019)
- [Efficient and Probabilistic Adaptive Voxel Mapping for Accurate Online LiDAR Odometry](https://mlsanity.com/paper/2109.07082/) (2021)
- [FusionPortable: A Multi-Sensor Campus-Scene Dataset for Evaluation of Localization and Mapping Accuracy on Diverse Platforms](https://mlsanity.com/paper/2208.11865/) (2022)
- [FusionPortableV2: A Unified Multi-Sensor Dataset for Generalized SLAM Across Diverse Platforms and Scalable Environments](https://mlsanity.com/paper/2404.08563/) (2024)
- [Robust Odometry and Mapping for Multi-LiDAR Systems with Online Extrinsic Calibration](https://mlsanity.com/paper/2010.14294/) (2020)
- [Learning-based Localizability Estimation for Robust LiDAR Localization](https://mlsanity.com/paper/2203.05698/) (2022)
- [Greedy-Based Feature Selection for Efficient LiDAR SLAM](https://mlsanity.com/paper/2103.13090/) (2021)
- [On Bundle Adjustment for Multiview PointCloud Registration](https://mlsanity.com/paper/2108.02976/) (2021)
- [FusionPlanner: A Multi-task Motion Planner for Mining Trucks via Multi-sensor Fusion](https://mlsanity.com/paper/2308.06931/) (2023)
- [LION: Lidar-Inertial Observability-Aware Navigator for Vision-Denied Environments](https://mlsanity.com/paper/2102.03443/) (2021)
- [Heterogeneous LiDAR Dataset for Benchmarking Robust Localization in Diverse Degenerate Scenarios](https://mlsanity.com/paper/2409.04961/) (2024)
- [Informed, Constrained, Aligned: A Field Analysis on Degeneracy-aware Point Cloud Registration in the Wild](https://mlsanity.com/paper/2408.11809/) (2024)
- [LiteVLoc: Map-Lite Visual Localization for Image Goal Navigation](https://mlsanity.com/paper/2410.04419/) (2024)
- [Accelerating Certifiable Estimation with Preconditioned Eigensolvers](https://mlsanity.com/paper/2207.05257/) (2022)
- [MS-Mapping: An Uncertainty-Aware Large-Scale Multi-Session LiDAR Mapping System](https://mlsanity.com/paper/2408.03723/) (2024)
- [RELEAD: Resilient Localization with Enhanced LiDAR Odometry in Adverse Environments](https://mlsanity.com/paper/2402.18934/) (2024)
- [Probabilistic Degeneracy Detection for Point-to-Plane Error Minimization](https://mlsanity.com/paper/2410.10784/) (2024)

## Abstract (arXiv)

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