DCReg: Decoupled Characterization for Efficient Degenerate LiDAR Registration

Xiangcheng Hu¹ · Xieyuanli Chen² · Mingkai Jia¹ · Jin Wu ^3*
Ping Tan¹· Steven L. Waslander^4†

¹HKUST   ²NUDT   ³USTB    ⁴U of T
†Project lead *Corresponding author

DCReg (Decoupled Characterization for ill-conditioned Registration) is a principled framework that addresses ill-conditioned point cloud registration problems, achieving 20% - 50% accuracy improvement and 5-100 times speedup over state-of-the-art methods.

• Reliable ill-conditioning detection: Decouples rotation and translation via Schur complement decomposition for ill-conditioning detection，eliminating coupling effects that mask degeneracy patterns.
• Quantitative characterization: Maps mathematical eigenspace to physical motion space, revealing which and to what extent specific motions lack constraints
• Targeted mitigation: Employs targeted preconditioning that stabilizes only degenerate directions while preserving observable information.

DCReg seamlessly integrates with existing registration pipelines through an efficient PCG solver with a single interpretable parameter.

Timeline

2025/09/09: the preprint paper is online, baseline codes will be published first!

Methods

Baseline and dataset

Video demo

Scenarios	Characterization Example	Features
		Planar degeneracy, t0-t1-r2 degenerate, the main components of motion sources are X-Y-Yaw. e.g. t0 = 90.0% X + xx %Y + xx% Z. the related angles of X with t0 is 4.5 deg, that means X should be the main reason. see figure 16.
		narrow stairs, spares features cause this degeneracy. sometimes t2, sometimes r0-r1. see figure 17.
		narrow passage, r0-t0 or r0, depends on your measurements.
		rich features but within narrow environments. r0-t0 or r0.

Controlled Simulation Analysis

Real-world Performance Evaluation

localization and mapping

Degeneracy Characterization

Degeneracy Detection

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Ablation and Hybrid Analysis

Run-time analysis

Parameter

Citations

For referencing our work, please use:

@misc{hu2025dcreg,
      title={DCReg: Decoupled Characterization for Efficient Degenerate LiDAR Registration}, 
      author={Xiangcheng Hu and Xieyuanli Chen and Mingkai Jia and Jin Wu and Ping Tan and Steven L. Waslander},
      year={2025},
      eprint={2509.06285},
      archivePrefix={arXiv},
      primaryClass={cs.RO},
      url={https://arxiv.org/abs/2509.06285}, 
}

Acknowledgment

The authors gratefully acknowledge the valuable contributions that made this work possible.

• We extend special thanks to Dr. Binqian Jiang and Dr. Jianhao Jiao for their insightful discussions that significantly contributed to refining the theoretical framework presented in this paper.
• We also appreciate Mr. Turcan Tuna for his technical assistance with the baseline algorithm implementation.

Contributors