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Rectified Point Flow: Generic Point Cloud Pose Estimation
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Proposes Rectified Point Flow, a conditional generative model that learns a point-wise velocity field over noisy part point clouds, with an overlap-pretrained PTv3 encoder, to unify pairwise point cloud registration and multi-part shape assembly.
Problem
Estimating 6-DoF part poses from unposed point clouds for pairwise registration and multi-part shape assembly, where symmetry, part interchangeability, and combinatorial assemblies make pose regression ambiguous.
Approach
Cast pose estimation as conditional generation: rectified flow transports Gaussian-noised points to their assembled positions in Euclidean space, so poses are recovered via Procrustes/SVD; symmetry is handled implicitly by the loss invariance, and the encoder is pretrained with point-wise inter-part overlap prediction instead of mesh-based fracture simulation.
Key results
- On BreakingBad-Everyday, Ours (Joint) reduces RE to 7.4 deg vs 9.9 deg for GARF; on TwoByTwo, Ours (Joint) RE 13.2 deg and TE 3.0 cm vs GARF 22.1 deg and 7.1 cm.
- On ModelNet-40, Ours (Joint) achieves RE 0.93 deg and TE 0.002 vs GeoTransformer 1.58 deg and 0.018; on TUD-L Recall@5° 97.7% vs 90.0% for Diff-RPMNet.
- Zero-shot on Fractura, Ours achieves 64.4% average part accuracy vs 57.7% for GARF zero-shot.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| joint-train across datasets rather than train on BreakingBad-Everyday alone | Rectified Point Flow · BreakingBad-Everyday | RE: 9.6 -> 7.4 | Helped |
| joint-train across datasets rather than train on TwoByTwo alone | Rectified Point Flow · TwoByTwo | RE: 18.7 -> 13.2 | Helped |
| joint-train across datasets rather than train on ModelNet-40 alone | Rectified Point Flow · ModelNet-40 | RE: 1.37° to 0.93° | Helped |
| use overlap-detection pre-training instead of no pre-training (ablation) | PTv3 encoder for Rectified Point Flow · BreakingBad-Everyday | Part Acc: 79.5 -> 93.5 | Helped |
| use overlap-detection pre-training instead of instance-segmentation pre-training (ablation) | PTv3 encoder for Rectified Point Flow · BreakingBad-Everyday | Part Acc: 80.9 -> 93.5 | Helped |
| replace MLP encoder with PTv3 encoder without pre-training (ablation) | Rectified Point Flow · BreakingBad-Everyday | Part Acc: 68.3 -> 79.5 | Helped |
| replace overlap-pretrained PTv3 with Point-BERT completion-pretrained encoder (ablation) | Rectified Point Flow · PartNet-Assembly | Part Acc: 50.2% to 45.2% | Hurt |
| replace Rectified Flow with DDPM (ablation) | Rectified Point Flow · shape assembly and pairwise registration | RE: BreakingBad-E: 7.4 -> 13.0; TwoByTwo: 13.2 -> 17.2; PartNet-A: 21.8 -> 29.5; IKEA-M: 10.8 -> 21.4; TUD-L: 1.4 -> 2.6; Mo | Hurt |
| replace Rectified Flow with DDPM (ablation) | Rectified Point Flow · shape assembly and pairwise registration | TE: BreakingBad-E: 2.0 -> 3.5; TwoByTwo: 3.0 -> 10.1; PartNet-A: 14.8 -> 21.3; IKEA-M: 17.2 -> 19.2; TUD-L: 0.3 -> 0.5; Mode | Hurt |
| increase sampling steps from 1 to 50 (ablation) | Rectified Point Flow · PartNet-Assembly | Part Accuracy: 25.2 -> 54.6 | Helped |
| use anchor-free average evaluation instead of anchor-fixed evaluation (ablation) | Rectified Point Flow · BreakingBad-Everyday | Part Acc: 93.5 -> 90.2 | Hurt |
| use anchor-free best-of-3 instead of anchor-free average (ablation) | Rectified Point Flow · PartNet-Assembly | Part Acc: 45.3 -> 54.3 | Helped |
Surprising findings
- Joint training across datasets improves accuracy over dataset-specific training, notably on TwoByTwo (RE 18.7 to 13.2 deg), despite small dataset sizes.
- Rectified flow outperforms DDPM as the generative formulation in this setting, reducing RE by about 35%.
Limitations
- Focuses on object-centric point clouds; does not handle cluttered scenes or partial observations/occlusion.
- Some generated assemblies are geometrically plausible but mechanically nonfunctional, and very geometrically complex objects fail.
- Limited number of points handled, restricting use on large-scale objects; anchor-fixed evaluation provides privileged anchor pose, and anchor-free performance is much lower.
Experimental setup
Datasets: IKEA-Manual TwoByTwo PartNet-Assembly BreakingBad TUD-L ModelNet-40 Objaverse 1.0
Benchmarks: BreakingBad-Everyday TwoByTwo PartNet-Assembly IKEA-Manual TUD-L ModelNet-40 Fractura
Metrics: Rotation Error (RE) Translation Error (TE) Part Accuracy Recall @ 5° Recall @ 1cm Chamfer Distance Overlap Ratio Relative RMSE
Baselines: MSN SE(3)-Assembly Jigsaw PuzzleFusion++ GARF DCPNet RPMNet GeoTransformer Diff-RPMNet B-LSTM RGL-Net Huang et al.
Builds on: Rectified Flow GARF Point Transformer V3 Diffusion Transformer
Closest papers by meaning
- RGGT: A Generative-Prior-Guided Transformer for Unified Rigid and Non-Rigid Point Cloud Registration (ICML 2026 · similarity 0.89)
- RCP: Recurrent Closest Point for Point Cloud (CVPR 2022 · similarity 0.89)
- PointFlowNet: Learning Representations for Rigid Motion Estimation From Point Clouds (CVPR 2019 · similarity 0.89)
- Deformation and Correspondence Aware Unsupervised Synthetic-to-Real Scene Flow Estimation for Point Clouds (CVPR 2022 · similarity 0.88)
- PointNetLK: Robust & Efficient Point Cloud Registration Using PointNet (CVPR 2019 · similarity 0.88)
- PointMC: Multi-instance Point Cloud Registration based on Maximal Cliques (ICML 2024 · similarity 0.87)
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