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Learning Generalizable Shape Completion with SIM(3) Equivariance
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Proposes SIMECO, the first fully SIM(3)-equivariant shape completion network (built on AdaPoinTr with vector neurons and a transform-restoration path), evaluated on PCN, KITTI and OmniObject3D under a de-biased protocol.
Problem
Shape completion models trained on pre-aligned, canonicalized data leak pose and scale cues and collapse on raw, unaligned real scans; existing equivariant methods still rely on ground-truth centroids or scales for normalization.
Approach
Build every layer of a transformer-based completion network to be SIM(3)-equivariant: a translation- and scale-invariant VN-LayerNorm canonicalizes features, VN-attention reasons over similarity-invariant geometry, and a transform-restoration path reinjects translation and scale via residual connections.
Key results
- On PCN under de-biased protocol, SIMECO reaches average CD-l1 8.59 and F1 0.714, versus 9.54 / 0.661 for AdaPoinTr with SIM(3) augmentation (about 10% lower CD).
- On KITTI, MMD drops from 6.47 (AdaPoinTr, SIM(3) augmentation) to 5.35 (SIMECO), a 17% reduction, with no bounding-box normalization.
- On OmniObject3D, CD-l1 is 10.25 versus 11.90 for AdaPoinTr (about 14% lower) and F1 is 0.698 versus 0.664.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SIM(3)-equivariant SIMECO instead of the strongest reported augmentation baseline | Shape completion · PCN | CD-ℓ1: 9.58 -> 8.59 | Helped |
| Use SIM(3)-equivariant SIMECO instead of AdaPoinTr with SIM(3) augmentation | Shape completion · PCN | F1: 0.661 -> 0.714 | Helped |
| Use SIM(3)-equivariant SIMECO instead of AdaPoinTr with SIM(3) augmentation | PCN-trained model · KITTI | MMD: 6.468 -> 5.353 | Helped |
| Use SIMECO instead of AdaPoinTr with SIM(3) augmentation | PCN-trained model · OmniObject3D | CD-ℓ1: 11.90 -> 10.25 | Helped |
| Replace the VN-SPD constraint with standard VN layers, centering, and normalization (ablation) | SIMECO · PCN | CD-ℓ1: 8.59 -> 9.31 | Hurt |
| Replace the VN-SPD constraint with standard VN layers, centering, and normalization (ablation) | SIMECO · PCN | F1: 0.714 -> 0.673 | Hurt |
| Train without transform augmentation rather than with SIM(3) transforms (ablation) | SIMECO · PCN Car | CD-ℓ1: 8.88 -> 8.76 | No clear effect |
| Train without transform augmentation rather than with SIM(3) transforms (ablation) | SIMECO · PCN Car | F1: 0.705 -> 0.712 | No clear effect |
| Progressively replace non-equivariant encoder/decoder layers with SIM(3)-equivariant layers (ablation) | SIMECO · PCN Car | CD-ℓ1 | Mixed |
| Use full SIM(3) equivariance rather than rotation-plus-translation or rotation-plus-scale equivariance (ablation) | PCN-trained model · KITTI | Fidelity | Helped |
| Use full SIM(3) equivariance rather than rotation-plus-translation or rotation-plus-scale equivariance (ablation) | PCN-trained model · KITTI | MMD | Helped |
| Use input bounding-box extent rather than global category maximum for scale normalization (ablation) | AdaPoinTr · PCN | CD-ℓ1: 12.46 -> 9.97 | Helped |
Surprising findings
- AdaPoinTr without augmentation collapses under the de-biased protocol (CD-l1 60.23 under I/SIM(3)).
- Training on PCN with I, SO(3), SE(3), or SIM(3) transforms gives nearly identical test performance, suggesting explicit canonicalization of training data is unnecessary.
Limitations
- Computational overhead: vector-valued equivariant modules are roughly three times costlier than scalar layers, giving higher latency than non-equivariant baselines.
- Equivariance is defined per single partial scan; cross-view symmetries across different partial observations are not enforced.
- Cannot handle articulated or multi-object scenes; can confuse shapes that coincide under a similarity transform (e.g., chair back vs sofa).
Experimental setup
Datasets: PCN ShapeNet
Benchmarks: PCN KITTI OmniObject3D
Metrics: CD-l1 F1 Fidelity MMD
Baselines: EquivPCN SCARP ESCAPE AdaPoinTr PoinTr SeedFormer SnowflakeNet AnchorFormer ODGNet ConDor
Builds on: AdaPoinTr Vector Neurons VN-Transformer VN-DGCNN ESCAPE
Closest papers by meaning
- ESCAPE: Equivariant Shape Completion via Anchor Point Encoding (CVPR 2025 · similarity 0.88)
- Fostering Generalization in Single-View 3D Reconstruction by Learning a Hierarchy of Local and Global Shape Priors (CVPR 2021 · similarity 0.87)
- Learning 3D Shape Completion From Laser Scan Data With Weak Supervision (CVPR 2018 · similarity 0.87)
- Frame Averaging for Equivariant Shape Space Learning (CVPR 2022 · similarity 0.87)
- LaS-Comp: Zero-shot 3D Completion with Latent-Spatial Consistency (CVPR 2026 · similarity 0.87)
- DinoComplete: 3D Shape Completion with Distilled Semantic Priors and State Space Models (NeurIPS 2026 · similarity 0.86)
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