Research map / Point clouds / Registration and matching
A robust inlier identification algorithm for point cloud registration via $\mathbf{\ell_0}$-minimization
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Reformulates point cloud registration as per-local-set alignment-error l0-minimization, solved via a two-stage decoupling (rotation/translation split plus null-space Bayesian relaxation) to identify inliers and pick the best hypothesis.
Problem
Point cloud registration with correspondences contaminated by high outlier ratios and noise, where accurate inlier identification is needed for robust rigid transformation estimation.
Approach
Formulates inlier identification as an l0-minimization of alignment errors over local sets built from a compatibility graph, decouples rotation from translation via relative point positions, and removes the other parameter with null-space matrices so that a Bayesian MAP closed-form (Frobenius-norm relaxation) identifies inliers.
Key results
- On KITTI with FPFH, the method reaches 99.56% registration recall, about 2% above MAC (97.66%).
- On 3DLoMatch with Predator descriptors, average registration recall is improved by about 7% over TR-DE, reaching 69.9% at 5000 correspondences.
- On the synthetic Bunny dataset, the method stays accurate at outlier ratios up to 90% and even 99%, where FGR, RANSAC, GORE and TEASER++ degrade.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ℓ0-minimization with two-stage decoupling for inlier identification | Point cloud registration · KITTI (FPFH) | RR (%): 99.46 -> 99.56 | Helped |
| Use ℓ0-minimization with two-stage decoupling for inlier identification | Point cloud registration · 3DMatch (3DSmoothNet) | RR (%): 94.82 -> 95.07 | Helped |
| Use ℓ0-minimization with two-stage decoupling for inlier identification | Point cloud registration · 3DMatch (FCGF) | TE (cm): 6.49 -> 6.48 | Helped |
| Vary the number of local sets (ablation) | Ours · KITTI | RR (%): 98.02 to 98.20 | No clear effect |
| Vary correspondences per local set (ablation) | Ours · KITTI | RR (%): 98.02 to 98.20 | No clear effect |
| Increase rotation inlier threshold KR (ablation) | Ours · KITTI | RR (%) | No clear effect |
| Increase translation inlier threshold Kt (ablation) | Ours · KITTI | RR (%) | No clear effect |
Limitations
- Fails on repeated patterns and textureless structures due to feature matching ambiguity.
- Two-stage decoupling strategy consumes about 95% of running time.
- Theory section lacks full assumptions and proofs.
Experimental setup
Datasets: Stanford Bunny KITTI 3DMatch 3DLoMatch
Benchmarks: KITTI 3DMatch 3DLoMatch Stanford Bunny
Metrics: registration recall rotation error translation error time
Baselines: FGR RANSAC GORE TEASER++ SC2-PCR MAC TR-DE TEAR DGR PointDSC VBReg EGST
Builds on: SC2-PCR MAC TEASER++ PointDSC TR-DE
Closest papers by meaning
- Inlier Confidence Calibration for Point Cloud Registration (CVPR 2024 · similarity 0.94)
- Reliable Inlier Evaluation for Unsupervised Point Cloud Registration (AAAI 2022 · similarity 0.93)
- Scalable 3D Registration via Truncated Entry-wise Absolute Residuals (CVPR 2024 · similarity 0.87)
- Registration is a Powerful Rotation-Invariance Learner for 3D Anomaly Detection (NeurIPS 2025 · similarity 0.87)
- PSReg: Prior-guided Sparse Mixture of Experts for Point Cloud Registration (AAAI 2025 · similarity 0.87)
- Multi-scale Consistency for Robust 3D Registration via Hierarchical Sinkhorn Tree (NeurIPS 2024 · similarity 0.87)
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