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

2025/10/30: Major revision, we foucs on polishing the logic of this paper.

2025/09/23: the baseline codes and data released, including ME-SR/ME-TSVD/ME-TReg/FCN-SR/O3D/XICP/SuperLoc!! This codes will help you deeply into the ICP process. Next we will show how to integrate these methods in your own SLAM systems.

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

Quick Start 1235`

Dependency (Test on Unbuntu 20.04)

Open3D 0.15.1	Ceres 2.1.0	yaml-cpp 0.6.2	Eigen 3.3.7	OpenMP 201511	TBB 2020.1	PCL 1.10.0

Install

mkdir build
cd build
cmake ..
make -j8

set the file path and parametes in icp.yaml, but if you want to do iterative experments, e.g. iterative for 5000, just use the icp_iter.yaml. if you want to test on the real-world data, just use the icp_pk01.yaml, like Figure.16 in the paper.

./icp_test_runner

For other settings, you can see the notes in the yaml. Note that, the impelment of SuperLoc and XICP has also verified using autodiff or NumericDiff methods. Finally you can get the output:

output files	results summary

If you want to plot the statistics results like the figures in our papers, we will provide later. If you want to integrate theses methods in your SLAM system, just make sure the degenercy handling only in the first iteration.

Test data: Cylinder and Parkinglot frames.

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

Important Issue

What you can get from the baseline codes?

• the efftect of different pose parameterization method for ICP, like SE(3), R3*SO(3), S3 and Eular.
• different implement of optimization, like eigen(mannually-derived), Ceres(autodiff and numerial method).
• different parallels method for ICP, like OpenMP and TBB.

Important theory For DCReg

Schur Conditioning

	S_R is precisely the Hessian of the rotation subproblem after optimally accommodating translation; hence spectral analysis on the rotation subproblem is equivalent (the sensitivity of φ) to analyzing the full problem with δt eliminated.
	This projection removes components of range(J_R) that can be explained by J_t, retaining only the rotation information that cannot be compensated by translation.
	This property demonstrates that Schur complementsnaturally eliminate sensitivity to unit or scale changes in the eliminated parameters, directly addressing the scale disparity between rotation (radians) and translation (meters)
	κ(S_R) may be smaller than κ(H_RR) when coupling is weak, or substantially larger when coupling is strong. (iv) shows that the real observability information can be masked by the cross terms (M_R and M_t).

Eigenvalue clamping in subspace

	This demonstrates why we clamp eigenvalues in subspace, but we do not set the cross term of Λ_R.
	We demonstrates eigenvalue clamping in a regularization view.

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 XICP implementation.

Contributors