Robust Single-Parameter Point Cloud Registration using Truncated Lp Functions

Seong Hun Lee; Patrick Vandewalle; Javier Civera

cs.CVOct 25, 2026

Robust Single-Parameter Point Cloud Registration using Truncated Lp Functions

Authors: Seong Hun Lee, Patrick Vandewalle, Javier Civera

Organizations: I3A, University of Zaragoza, 50018 Zaragoza, Spain · EAVISE, Department of Electrical Engineering, KU Leuven, 2860 Sint-Katelijne-Waver, Belgium

Abstract

We propose a novel method for robust point cloud registration with only one tunable parameter. Our method, dubbed TLP, uses truncated $L_p$ functions with different values of $p$ to assign priority scores to correspondences, select the hypothesis, and refine the final model. By leveraging the robustness of truncated functions, TLP effectively handles the high outlier rates commonly encountered in real-world 3D feature matching. We also exploit GPU parallelization to evaluate hypotheses efficiently, enabling registration from thousands of correspondences in under a second on average. With only one tunable parameter, our method offers greater practicality than multi-parameter methods that require dataset-specific tuning of several parameters. Evaluations on public benchmark datasets demonstrate that TLP achieves higher accuracy than state-of-the-art single-parameter methods. Furthermore, it outperforms two widely used multi-parameter methods on three of the four evaluated datasets while maintaining competitive runtime.

Figures & tables

Fig. 1: Normalized, truncated, smoothed

L_{p}

costs and scores versus residual

r

. The truncation threshold is denoted by

\delta

Fig. 2: [Top] Correct (solid green) and incorrect (dashed red) correspondences. [Bottom left] Truncated $L_{3}$ compatibility matrix (Sec. IV-B ). Shaded cells indicate stronger agreement. Red outlines mark accidental compatibilities of $c_{5}$ with $c_{2}$ and $c_{3}$ . [Bottom right] Initial support $\mathbf{w}=\mathbf{C}\mathbf{1}$ and aggregated scores $\mathbf{s}=\mathbf{C}\mathbf{w}$ . Both rank all correct matches above the incorrect ones. Aggregation increases the ratio of mean inlier-to-outlier ratio from $1.9$ to $2.28$ , improving their relative separation in this example.

	3DMatch		KITTI
Method	FPFH	FCGF	FPFH	FCGF
TEASER++	0.04	N/A	0.45	N/A
TEAR	0.07	0.07	0.4	2.1
HERE (w/o scaling)	0.07	0.07	0.7	1.8
HERE (with scaling)	0.07	0.07	0.7	1.7
PCR-99	0.02	0.01	0.25	0.4

TABLE I: Selected distance thresholds for each dataset–descriptor configuration, tuned by maximizing mAA at

15^{\circ}

. N/A denotes an unavailable setting.

Fig. 3: Qualitative comparison on five point-cloud pairs from 3DMatch using FPFH descriptors. The two point clouds are shown in blue and orange. TLP produces alignments closely matching the ground truth, while the single-parameter baselines exhibit varying degrees of misalignment. Red circles highlight selected alignment errors.

		Multi-Parameter		Single-Parameter
Dataset	Metric	SC 2 -PCR	MAC	TEASER++	TEAR	HERE (with scaling)	HERE (w/o scaling)	PCR-99	TCF	TLP (Ours)
3DMatch + FPFH	mAA at $5^{\circ}$	0.5861	Out of memory	0.5503	0.3257	0.4731	0.4734	0.5110	0.5540	0.5879
	mAA at $10^{\circ}$	0.7129		0.6747	0.3835	0.5587	0.5596	0.6316	0.6808	0.7002
	mAA at $15^{\circ}$	0.7649		0.7272	0.4118	0.5968	0.5979	0.6848	0.7321	0.7456
3DMatch + FCGF	mAA at $5^{\circ}$	0.6612	0.6662	Excessive runtime (some $>2$ h)	0.5569	0.6430	0.6442	0.6237	0.6295	0.6818
	mAA at $10^{\circ}$	0.7955	0.7977		0.6734	0.7622	0.7631	0.7619	0.7619	0.8048

TABLE II: Rotation-based registration accuracy (mAA) across different datasets and features. Higher values indicate better performance, with a maximum of 1. The best available result in each row is highlighted in blue and bold.

	Multi-Parameter		Single-Parameter
Dataset	SC 2 -PCR	MAC	TEASER++	TEAR	HERE (with scaling)	HERE (w/o scaling)	PCR-99	TCF	TLP (Ours)
3DMatch + FPFH	0.24 s	Out of memory	1.45 s	1.64 s	1.87 s	2.21 s	0.68 s	0.30 s	0.36 s
3DMatch + FCGF	0.24 s	11.46 s	Sometimes $>2$ h	0.99 s	1.06 s	1.49 s	0.22 s	2.68 s	0.20 s
KITTI + FPFH	0.71 s	Out of memory	1.46 s	3.53 s	2.02 s	4.80 s	0.19 s	0.10 s	0.65 s
KITTI + FCGF	0.73 s	22.46 s	Often $>0.5$ h	0.29 s	1.19 s	3.21 s	0.18 s	39.33 s	0.40 s

TABLE III: Runtime comparison. The fastest result on each dataset is shown in blue and bold.

Dataset	Metric	TLP (Default)	Without $1.2$ factor for $\tau$	Without $q=0.1$	Without $q=0.2$	Without $q=0.3$	Without $q=0.4$	Without $L_{2}$ refinement	Without $L_{0^{+}}$ refinement	Without $L_{0.4}$ refinement
3DMatch + FPFH	mAA at $5^{\circ}$	0.5879	0.5813	0.5875	0.5845	0.5864	0.5850	0.5809	0.5774	0.5791
	mAA at $10^{\circ}$	0.7002	0.6958	0.6962	0.6952	0.6988	0.6966	0.6944	0.6861	0.6948
	mAA at $15^{\circ}$	0.7456	0.7420	0.7405	0.7397	0.7441	0.7413	0.7401	0.7299	0.7416
3DMatch + FCGF	mAA at $5^{\circ}$	0.6818	0.6792	0.6817	0.6819	0.6821	0.6822	0.6812	0.6826	0.6764
	mAA at $10^{\circ}$	0.8048	0.8032	0.8047	0.8046	0.8047	0.8044	0.8033	0.8052	0.8017
	mAA at $15^{\circ}$	0.8517	0.8506	0.8516	0.8515	0.8516	0.8512	0.8495	0.8518	0.8497

TABLE IV: Ablation study: Each variant removes the indicated setting or refinement step from the default configuration. Performance is measured by rotation-based registration accuracy (mAA). Higher values indicate better performance, with a maximum of 1. The best available result in each row is highlighted in blue and bold.

Point Cloud Registration

Point cloud registration aligns 3D point sets by estimating the transformations and correspondences that make their geometry consistent.

See all 110 papers

Sinkhorn-CPD: Robust point cloud registration via unbalanced entropic optimal transport
Jun 15, 2026Jin Zhang, Mingyang Zhao, Bing Liu +1Point Cloud Registration Optimal Transport
LMIB & School of Mathematical Sciences, Beihang University, Beijing, China · State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China · University of Chinese Academy of Sciences, Beijing, China +1
PARTE: Plane-Assisted Robust Transformation Estimation for Point Cloud Registration
Sep 21, 2026Abolfazl Babanazari, Carson Cramer, Tyler Summers +2Point Cloud Registration
Department of Computer Science, Colorado School of Mines. · Department of Mechanical Engineering, University of Texas at Dallas. · U.S. Army Combat Capabilities Development Command, Army Research Laboratory
IGASA: Integrated Geometry-Aware and Skip-Attention Modules for Enhanced Point Cloud Registration
Mar 13, 2026Dongxu Zhang, Jihua Zhu, Shiqi Li +4Point Cloud Registration Point Cloud Learning

Jun 15, 2026J/K move · Enter open · S save

Sinkhorn-CPD: Robust point cloud registration via unbalanced entropic optimal transport

Jin Zhang, Mingyang Zhao, Bing Liu, Xin Jiang

LMIB & School of Mathematical Sciences, Beihang University, Beijing, China · State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China · University of Chinese Academy of Sciences, Beijing, China+1

Point Cloud Registration Optimal Transport

Open paper AskPDF arXiv

Coherent Point Drift (CPD) is widely used for rigid point cloud registration because of its soft correspondences and closed-form parameter updates. However, CPD's target-side marginal constraint forces every observation, including outliers, to receive exactly unit probability mass. This assumption degrades registration accuracy under heavy outliers and partial overlap. Optimal transport (OT) methods can handle missing mass through unbalanced formulations, but require hand-tuned annealing schedules. In this paper, we propose Sinkhorn-CPD, which replaces CPD's target-side marginal constraint with dual Kullback-Leibler penalties, allowing the algorithm to discard outliers on both sides. The resulting formulation is a fully unbalanced entropic optimal transport problem, which can be efficiently solved by generalized Sinkhorn iterations. Moreover, Sinkhorn-CPD preserves the closed-form Procrustes and variance updates of CPD. In our method, the variance sigma^2 plays the role of the entropic regularization parameter, which induces an automatic annealing schedule from diffuse to sharp correspondences without manual temperature tuning. Experiments on synthetic, cross-category, and scan-to-CAD benchmarks show that Sinkhorn-CPD achieves state-of-the-art accuracy, with strong robustness to outliers and partial overlap.

Abstract

Point Cloud Registration

Explore similar work

Sinkhorn-CPD: Robust point cloud registration via unbalanced entropic optimal transport

PARTE: Plane-Assisted Robust Transformation Estimation for Point Cloud Registration

IGASA: Integrated Geometry-Aware and Skip-Attention Modules for Enhanced Point Cloud Registration