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Denoising Point Clouds in Latent Space via Graph Convolution and Invertible Neural Network
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Proposes PD-LTS, a point cloud denoiser that uses an invertible monotone-operator neural network fused with multi-level graph convolution (MLGC) to disentangle noise in latent space, masks noise channels, and inverts to get clean points.
Problem
Point clouds captured by LiDAR or structured light contain noise and outliers that hurt downstream tasks; displacement-regression denoisers over-smooth or collapse surfaces, and prior flow-based denoisers lack strong local shape feature extraction.
Approach
Model a bijective mapping between noisy point clouds and a latent space with an invertible monotone-operator network (Lipschitz-constrained residual blocks) conditioned on densely connected EdgeConv features, so noise is isolated in specific latent channels that can be zeroed before inverting back to 3D; trained with EMD reconstruction loss instead of likelihood.
Key results
- On PUNet 10K points with 1% noise, the light version reaches CD 18.25 and P2M 4.96 (x10^-5), beating IterativePFN (CD 20.56, P2M 5.01).
- The heavy version achieves CD 24.41 and P2M 7.58 on 50K points at 2% noise, and CD 8.63 / P2M 5.81 at 50K, 2.5% noise, the best among compared methods.
- Uniformity comparison on 10K points shows the heavy version has much lower uniformity error than Score, PD-flow and IterativePFN across all noise levels.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the heavy version instead of IterativePFN | Point-cloud denoising · PUNet 10K and 50K, 1%, 2%, and 2.5% noise | CD and P2M: CD: 20.56 -> 17.81; 30.43 -> 24.41; 33.52 -> 26.99; 6.05 -> 4.70; 8.03 -> 6.46; 10.15 -> 8.63. P2M: 5.01 -> 4.65; 8.45 - | Helped |
| Add MLGC (ablation) | Proposed light denoising framework · PUNet 10K, 1% noise | CD: 25.93 -> 18.25 | Helped |
| Add stage 2 of MLGC (ablation) | Proposed light denoising framework · PUNet 10K, 1% noise | CD: 18.42 -> 18.25 | Helped |
| Use more than 1 invertible layer (ablation) | Proposed light denoising framework · PUNet 10K, 1% noise | CD: 23.01 -> 18.25 | Helped |
| Use more than 6 invertible layers (ablation) | Proposed light denoising framework · PUNet 10K, 1% noise | CD: 18.35 -> 18.25 | Helped |
| Use augmented dimension 48 instead of 8 (ablation) | Proposed light denoising framework · PUNet 10K, 1% noise | CD: 18.59 -> 18.25 | Helped |
| Use augmented dimension 48 instead of 64 (ablation) | Proposed light denoising framework · PUNet 10K, 2.5% noise | CD: 28.61 -> 28.49 | Helped |
Surprising findings
- Increasing augmented dimension from 48 to 64 gives minimal improvement and slightly worsens generalization at 2.5% noise.
- Displacement-based supervision via nearest-point matching is argued to miss clean points; EMD bijective supervision is claimed to improve uniformity.
Limitations
- Heavy version uses three stacked denoising modules, increasing cost relative to light version.
- Method evaluated mainly on synthetic Gaussian noise; real-world evaluation is qualitative only on Paris-rue-Madame.
Experimental setup
Datasets: PUNet Paris-rue-Madame
Benchmarks: PUNet Paris-rue-Madame
Metrics: Chamfer distance point-to-mesh distance uniformity
Baselines: PCN GPDNet DMRDenoise PD-flow ScoreDenoise PointFilter IterativePFN
Builds on: DGCNN invertible monotone operator networks PD-flow IterativePFN EdgeConv
Closest papers by meaning
- You Should Learn to Stop Denoising on Point Clouds in Advance (AAAI 2025 · similarity 0.86)
- U-CAN: Unsupervised Point Cloud Denoising with Consistency-Aware Noise2Noise Matching (NeurIPS 2025 · similarity 0.84)
- TIGER: Time-Varying Denoising Model for 3D Point Cloud Generation with Diffusion Process (CVPR 2024 · similarity 0.84)
- 3DMambaIPF: A State Space Model for Iterative Point Cloud Filtering via Differentiable Rendering (AAAI 2025 · similarity 0.83)
- PointInfinity: Resolution-Invariant Point Diffusion Models (CVPR 2024 · similarity 0.83)
- A Conditional Denoising Diffusion Probabilistic Model for Point Cloud Upsampling (CVPR 2024 · similarity 0.82)
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