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APML: Adaptive Probabilistic Matching Loss for Robust 3D Point Cloud Reconstruction
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Proposes APML, a fully differentiable soft one-to-one point cloud loss using adaptive-temperature softmax and Sinkhorn normalization, evaluated on completion (PCN, ShapeNet) and WiFi-CSI point cloud generation.
Problem
Chamfer-based losses (CD, HyperCD, InfoCD, DCD) use nearest-neighbor assignments that cause many-to-one correspondences, point clumping and poor sparse-region coverage, while EMD is one-to-one but cubic cost and impractical for deep training.
Approach
Approximate one-to-one matching with a soft transport plan: per-row/column adaptive softmax whose temperature is set analytically so the best match gets at least p_min probability, followed by symmetrization and a fixed number of Sinkhorn normalizations; the loss is the expected cost under this plan.
Key results
- On PCN with FoldingNet, APML reduces EMD×100 to 5.34 versus 28.71 for CD and 22.93 for HyperCD (F1 0.56 vs 0.43 for CD).
- On MM-Fi WiFi-CSI generation with CSI2PC, APML achieves EMD×100 of 14.112 versus 34.198 (CD) and 35.188 (InfoCD), with CD 0.152 vs 0.147 for InfoCD.
- APML adds roughly 15-30% training time over CD; memory is higher due to the dense pairwise cost matrix (about 1.8 GB for 16k points).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Train with APML instead of the strongest listed baseline | PCN · PCN / PCN backbone | EMD*100: 5.54 -> 4.72 | Helped |
| Train with APML instead of the strongest listed baseline | FoldingNet · PCN | EMD*100: 21.24 -> 5.34 | Helped |
| Train with APML instead of the strongest listed baseline | PoinTr · PCN | EMD*100: 8.79 -> 5.62 | Helped |
| Train with APML instead of the strongest listed baseline | FoldingNet · ShapeNet-55 | EMD*100: 19.55 -> 9.07 | Helped |
| Train with APML instead of the strongest listed baseline | PoinTr · ShapeNet-55 | EMD*100: 7.55 -> 6.08 | Helped |
| Train with APML instead of the strongest listed baseline | FoldingNet · ShapeNet-34 | EMD*100: 16.53 -> 9.49 | Helped |
| Train with APML instead of the strongest listed baseline | PoinTr · ShapeNet-34 | EMD*100: 11.88 -> 8.14 | Helped |
| Train with APML instead of the strongest listed baseline | FoldingNet · SN Unseen-21 | EMD*100: 19.27 -> 10.42 | Helped |
| Train with APML instead of the strongest listed baseline | PoinTr · SN Unseen-21 | EMD*100: 12.89 -> 9.19 | Helped |
| Train with APML instead of the strongest listed baseline | CSI2PC · MM-Fi | EMD*100: 34.198 -> 14.112 | Helped |
| Train with APML instead of HyperCD | PCN · PCN / PCN backbone | F1: 0.64 -> 0.62 | Hurt |
| Train with APML instead of InfoCD | FoldingNet · PCN | F1: 0.54 -> 0.56 | Helped |
Surprising findings
- APML increases CD-L1/L2 on the PoinTr backbone relative to HyperCD despite lower EMD and better visual quality.
- The CD-based losses, despite lower CD values, produce visibly worse reconstructions with clumping and missing structures.
Limitations
- Memory scales quadratically with point count; the dense cost matrix limits batch size.
- Introduces a single hyperparameter p_min (fixed at 0.8, not tuned), whose sensitivity is not studied.
- Evaluated only on synthetic completion sets and one real generation set; not tested on real-scan completion datasets such as ScanNet or KITTI.
Experimental setup
Datasets: PCN ShapeNet-34 ShapeNet-55 MM-Fi
Benchmarks: PCN ShapeNet-34 ShapeNet-55 ShapeNet Unseen-21 MM-Fi
Metrics: F1 EMD Chamfer Distance CD-L1 CD-L2
Baselines: CD HyperCD InfoCD DCD EMD
Builds on: Chamfer distance Sinkhorn-Knopp Earth Mover's Distance HyperCD InfoCD
Closest papers by meaning
- DV-Matcher: Deformation-based Non-rigid Point Cloud Matching Guided by Pre-trained Visual Features (CVPR 2025 · similarity 0.88)
- Adaptive 3D Reconstruction via Diffusion Priors and Forward Curvature-Matching Likelihood Updates (NeurIPS 2025 · similarity 0.87)
- A Computation-Aware Shape Loss Function for Point Cloud Completion (AAAI 2024 · similarity 0.87)
- A Consistency-Aware Spot-Guided Transformer for Versatile and Hierarchical Point Cloud Registration (NeurIPS 2024 · similarity 0.87)
- DiffCorr: Conditional Diffusion Model with Reliable Pseudo-Label Guidance for Unsupervised Point Cloud Shape Correspondence (AAAI 2025 · similarity 0.86)
- Adaptive Siamese Masked Autoencoder with Global Optimization for Unsupervised Point Cloud Shape Correspondence (AAAI 2025 · similarity 0.86)
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