Research map / Point clouds / Shape and surface completion
Unpaired Point Cloud Completion via Unbalanced Optimal Transport
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Formulates unpaired point cloud completion as an unbalanced optimal transport map problem and learns it with a neural OT max-min objective using an InfoCD cost, a source mixture trick, and a GAN-like backbone.
Problem
Unpaired point cloud completion, where incomplete and complete point clouds are sampled independently without correspondences, and class imbalance between the two sets degrades existing methods.
Approach
Treats unpaired completion as an unbalanced optimal transport map problem learned with a neural semi-dual objective, selects the InfoCD cost by analysing cost-minimizer retrieval quality, and mixes complete samples into the source distribution to remain robust to class imbalance.
Key results
- Single-category USSPA AVG cdl1 of 7.60 (x10^-2), best among unpaired methods (USSPA 8.56).
- On PCN single-category AVG cdl1 of 7.87 versus USSPA 12.63 among unpaired methods.
- Under class-imbalance ablation, UOT-UPC cdl1 stays between 6.75 and 6.94 while USSPA varies from 6.97 to 8.08.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use UOT-UPC instead of USSPA | Unpaired point cloud completion · USSPA, single-category (AVG) | cdl1 × 102 (↓): 8.56 -> 7.60 | Helped |
| use UOT-UPC instead of USSPA | Unpaired point cloud completion · USSPA, multi-category | F 0.1% score: 16.88 -> 19.25 | Helped |
| use UOT-UPC instead of USSPA | Unpaired point cloud completion · USSPA, multi-category | F 1% score: 72.31 -> 71.52 | Hurt |
| replace InfoCD with l2 cost (ablation) | UOT-UPC · USSPA, multi-category (trash bin and TV) | cdl1 × 102 (↓): 8.83 -> 24.16; 6.07 -> 23.71 | Hurt |
| replace InfoCD with cdl2 cost (ablation) | UOT-UPC · USSPA, multi-category (trash bin and TV) | cdl1 × 102 (↓): 8.83 -> 10.40; 6.07 -> 6.47 | Hurt |
| replace InfoCD with cdl2fwd cost (ablation) | UOT-UPC · USSPA, multi-category (trash bin and TV) | cdl1 × 102 (↓): 8.83 -> 10.16; 6.07 -> 7.39 | Hurt |
| add complete samples to the source using the mixture trick (ablation) | UOT-UPC · USSPA, single-category | cdl1: 7.94 -> 7.60 | Helped |
| add complete samples to the source using the mixture trick (ablation) | UOT-UPC · USSPA, single-category | F 0.1% score: 18.12 -> 18.43 | Helped |
| add complete samples to the source using the mixture trick (ablation) | UOT-UPC · USSPA, single-category | F 1% score: 73.49 -> 75.59 | Helped |
| add complete samples to the source using the mixture trick (ablation) | UOT-UPC · USSPA, multi-category | cdl1: 8.98 -> 8.96 | Helped |
| add complete samples to the source using the mixture trick (ablation) | UOT-UPC · USSPA, multi-category | F 0.1% score: 18.04 -> 19.25 | Helped |
| add complete samples to the source using the mixture trick (ablation) | UOT-UPC · USSPA, multi-category | F 1% score: 71.75 -> 71.52 | Hurt |
Surprising findings
- The standard OT variant (OT-UPC) performs much worse than USSPA under class imbalance (cdl1 about 23 to 30), showing that unbalanced relaxation is essential.
Limitations
- Training is unstable due to adversarial max-min optimization, as in GANs.
- Only hand-designed cost functions were explored; learned neural cost functions were left for future work.
- Multi-category F1% score is comparable rather than best.
Experimental setup
Datasets: USSPA PCN ShapeNet KITTI
Benchmarks: USSPA PCN KITTI
Metrics: L1 Chamfer distance (cdl1) F-score F0.1% F-score F1%
Baselines: USSPA ShapeInv Unpaired (Chen et al., 2020) Cycle4 PoinTr Disp3D TopNet OT-UPC
Builds on: Neural OT (Rout et al., 2022) UOTM (Choi et al., 2023) USSPA InfoCD
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