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Where Precision Meets Efficiency: Transformation Diffusion Model for Point Cloud Registration
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Proposes a Transformation Diffusion Model (TDM) that casts point cloud registration as denoising diffusion over quaternion rotation and translation, acting as a plug-and-play module on top of PCRNet and RPMNet.
Problem
Point cloud registration faces a trade-off between precision (correspondence-based methods) and efficiency (correspondence-free methods, or iterative refinement that repeatedly re-encodes the source cloud).
Approach
Diffuse ground-truth rotation (as quaternion) and translation in separate linear spaces (H and R3) rather than on the SE(3) manifold, map the noisy transformation into a latent feature via a Transformation Encoder fused with source features, and train a denoiser that predicts the clean transformation with DDIM-style sampling; the module plugs into existing registration networks.
Key results
- On ModelNet40 completely overlapping, TDM-RPMNet reduces RMSE(R) from 8.0357 to 1.1064 versus RPMNet (about 86% improvement).
- TDM-PCRNet reduces ModelNet40 MAE(R) from 10.2498 to 1.6935 and run time from 1.2318 s to under 1e-7 s per the reported table.
- On KITTI, TDM-RPMNet reduces RMSE(R) from 35.9824 to 0.8222 versus RPMNet.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add TDM to RPMNet | RPMNet · ModelNet40, completely overlapping | RMSE(R): 8.0357 -> 1.1064 | Helped |
| Add TDM to PCRNet | PCRNet · ModelNet40, completely overlapping | RMSE(R): 19.8457 -> 3.3411 | Helped |
| Add TDM to RPMNet | RPMNet · ModelNet40, partially overlapping | RMSE(R): 11.0629 -> 3.8624 | Helped |
| Add TDM to RPMNet | RPMNet · KITTI | RMSE(R): 35.9824 -> 0.8222 | Helped |
| Add TDM to RPMNet | RPMNet · 3DMatch | RMSE(R): 21.1454 -> 0.1864 | Helped |
| Add TDM to RPMNet | RPMNet · ModelNet40, completely overlapping | Time(s): 0.1626 -> 0.0298 | Helped |
| Represent rotation with quaternions instead of Euler angles (ablation) | TDM-PCRNet · ModelNet40, completely overlapping | MAE(R): 13.7668 -> 1.6935 | Helped |
| Fuse transformation features with template features instead of source features (ablation) | TDM-PCRNet · ModelNet40, completely overlapping | MAE(R): 1.6935 -> 1.7959 | No clear effect |
| Concatenate transformation, source, and template features (ablation) | TDM-PCRNet · ModelNet40, completely overlapping | MAE(R) | Hurt |
Surprising findings
- Diffusing Euler angles plus translation (R3 and R3) instead of quaternion plus translation degrades TDM-PCRNet badly (MAE(R) 13.77 vs 1.69), which the authors attribute to scale disparity between angles and translation.
- Concatenating all noisy-transformation, source, and template features fails to converge and is unstable.
Limitations
- Relies on the embedded network's own loss and architecture; gains are demonstrated only on PCRNet and RPMNet variants.
- Euler-angle parameterization was not workable, indicating sensitivity to the choice of transformation representation.
- Timing for the TDM-PCRNet entry is reported as under 1e-7 s, which is implausibly small and is not clearly explained.
Experimental setup
Datasets: ModelNet40 3DMatch KITTI
Benchmarks: ModelNet40 3DMatch KITTI
Metrics: RMSE MAE ERROR (isotropic) run time
Baselines: ICP FGR PointNetLK PCRNet DeepGMR DCP FMR RPMNet RORNet REGTR
Builds on: DDPM DDIM PCRNet RPMNet DCP
Closest papers by meaning
- FreeReg: Image-to-Point Cloud Registration Leveraging Pretrained Diffusion Models and Monocular Depth Estimators (ICLR 2024 · similarity 0.90)
- TIGER: Time-Varying Denoising Model for 3D Point Cloud Generation with Diffusion Process (CVPR 2024 · similarity 0.88)
- PosDiffNet: Positional Neural Diffusion for Point Cloud Registration in a Large Field of View with Perturbations (AAAI 2024 · similarity 0.88)
- DiffCorr: Conditional Diffusion Model with Reliable Pseudo-Label Guidance for Unsupervised Point Cloud Shape Correspondence (AAAI 2025 · similarity 0.88)
- Point Cloud Pre-training with Diffusion Models (CVPR 2024 · similarity 0.88)
- PointInfinity: Resolution-Invariant Point Diffusion Models (CVPR 2024 · similarity 0.87)
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