Research map / Point clouds / Shape and surface completion
A Computation-Aware Shape Loss Function for Point Cloud Completion
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Proposes AAIP, an auction-based EMD approximation for point cloud completion loss that uses provably valid initial prices computed from a successive-shortest-path local assignment plus adaptive iteration limits.
Problem
Exact EMD is too expensive to use as a training loss for point cloud completion, while existing EMD approximations (emd1, emd2) deviate substantially from true EMD and slow or noisy training.
Approach
Initialize auction-algorithm sink prices with provably valid initial prices (Definition 1, Theorem 1) derived from a local assignment computed via successive shortest path with a simplified-graph incremental algorithm, and add an adaptive iteration budget tied to data characteristics, so the auction converges faster to the same assignment as the unmodified auction.
Key results
- On sparse (1024-point) clouds, AAIP reduces MSE of the EMD estimate to 121.79 versus 1388.26 (emd1) and 912.78 (emd2).
- Training MSN with AAIP instead of emd2 lowers average EMD from 30.68 to 27.71 (x1e-3) on ShapeNet.
- Training PCN with AAIP on the coarse output lowers average EMD from 55.29 (emd1) to 46.60, and CD+AAIP reaches 39.17.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use AAIP instead of emd2 as the loss | MSN · ShapeNet, average | EMD×103: 30.68 -> 27.71 | Helped |
| Use AAIP instead of emd2 as the loss | MSN · ShapeNet, all eight categories | EMD×103: 33.12 -> 28.99; 31.12 -> 28.25; 31.11 -> 28.48; 36.13 -> 34.18; 36.66 -> 31.53; 32.90 -> 31.45; 18.70 -> 16.58; 25.66 -> | Helped |
| Use AAIP for coarse output loss instead of CD or emd1 | PCN · ShapeNet, average | EMD×103: 60.93 -> 46.60; 55.29 -> 46.60 | Helped |
| Use AAIP for dense output loss instead of CD | PCN · ShapeNet, average | EMD×103: 60.93 -> 39.17 | Helped |
| Replace emd2 with AAIP for EMD estimation | EMD approximation on dense point clouds (8192 points) · Dense point clouds (8192 points) | MSE: 1131.23 -> 408.13 | Helped |
| Add the adaptive iteration strategy (ablation) | AIP · Point clouds of varying sizes | EMD estimation accuracy and efficiency | Helped |
| Add initial prices to the auction algorithm (ablation) | Auction algorithm for EMD approximation · Point clouds of varying sizes | EMD estimation accuracy | Helped |
Surprising findings
- Initial prices from a local assignment preserve the exact auction assignment while reducing iterations, yet the approximation also beats emd1 even though emd1 is the fastest method.
Limitations
- Accuracy-time tradeoff: emd1 is faster than AAIP, and AAIP is slower than emd2 by a minimal but nonzero margin.
- Adaptive iteration budget depends on heuristic scale factor and edge limits set by point cloud size.
Experimental setup
Datasets: ShapeNet
Benchmarks: ShapeNet
Metrics: EMD mean squared error of EMD estimate runtime
Baselines: emd1 (Fan et al. 2017) emd2 (MSN auction-based EMD) CD
Builds on: Earth Mover's Distance loss (Fan et al. 2017) auction algorithm (Bertsekas) MSN PCN Simplified Graph Incremental Algorithm
Closest papers by meaning
- Morphing and Sampling Network for Dense Point Cloud Completion (AAAI 2020 · similarity 0.88)
- APML: Adaptive Probabilistic Matching Loss for Robust 3D Point Cloud Reconstruction (NeurIPS 2025 · similarity 0.87)
- FSC: Few-point Shape Completion (CVPR 2024 · similarity 0.86)
- SPU-IMR: Self-supervised Arbitrary-scale Point Cloud Upsampling via Iterative Mask-recovery Network (AAAI 2025 · similarity 0.85)
- Orthogonal Dictionary Guided Shape Completion Network for Point Cloud (AAAI 2024 · similarity 0.85)
- DC-PCN: Point Cloud Completion Network with Dual-Codebook Guided Quantization (AAAI 2025 · similarity 0.85)
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