Research map / Point clouds / Shape and surface completion
ESCAPE: Equivariant Shape Completion via Anchor Point Encoding
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Proposes ESCAPE, a rotation-equivariant point cloud shape completion method that encodes partial shapes as distances to curvature-selected anchor points and decodes them with a modified AdaPoinTr transformer followed by coordinate optimization.
Problem
Shape completion methods rely on canonical poses or canonical coordinates and degrade severely under arbitrary rotations of partial point clouds.
Approach
Represent points by their Euclidean distances to k curvature-selected anchor points (rotation-invariant), process these distance features with a modified AdaPoinTr transformer to predict distances of the complete shape, and recover coordinates by least-squares optimization, yielding rotation-equivariant completions without pose estimation.
Key results
- On PCN with rotated inputs canonicalized by ConDor, ESCAPE averages 10.58 CD-L1 versus 14.07 for SeedFormer and 66.40 for AnchorFormer (best baseline is SeedFormer).
- On OmniObject3D with unknown poses, ESCAPE reaches 18.82 median CD-L1 average versus 29.56 for SeedFormer (best baseline).
- On KITTI cars with rotated inputs, ESCAPE achieves MMID 5.93 versus 6.15 for PoinTr and 16.08 for SnowflakeNet, with fidelity 1.81.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use anchor-point distance encoding in place of canonical-coordinate processing | ESCAPE · PCN rotated inputs | CD-L1 (×1000): 14.07 -> 10.58 | Helped |
| Use anchor-point distance encoding for completion on real-world scans | ESCAPE · OmniObject | median CD-L1 (×1000): 29.56 -> 18.82 | Helped |
| Use ESCAPE for rotated car completion | ESCAPE · KITTI Cars rotated inputs | MMID (CD-L2 ×1000): 6.15 -> 5.93 | Helped |
| Replace the baseline encoding with ESCAPE's anchor-point encoding | PCN rotated inputs · PCN rotated inputs | CD-L1 (×1000): 124.0 -> 10.58 | Helped |
| Replace Vector Neuron encoding with ESCAPE's anchor-point encoding | PCN rotated inputs · PCN rotated inputs | CD-L1 (×1000): 18.62 -> 10.58 | Helped |
| Replace PPF encoding with ESCAPE's anchor-point encoding | PCN rotated inputs · PCN rotated inputs | CD-L1 (×1000): 17.46 -> 10.58 | Helped |
| Add curvature-based Ball Query anchor refinement with radius 0.075 (ablation) | ESCAPE · PCN subset | CD-L1 (×1000): 14.74 -> 13.58 | Helped |
| Use curvature-based Ball Query anchor refinement with radius 0.05 (ablation) | ESCAPE · PCN subset | CD-L1 (×1000): 14.74 -> 14.23 | Helped |
| Increase Ball Query anchor-refinement radius from 0.075 to 0.1 (ablation) | ESCAPE · PCN subset | CD-L1 (×1000): 13.58 -> 15.00 | Hurt |
| Increase Ball Query anchor-refinement radius from 0.075 to 0.15 (ablation) | ESCAPE · PCN subset | CD-L1 (×1000): 13.58 -> 15.76 | Hurt |
| Replace Ball Query anchor refinement with clustering at threshold 0.0 (ablation) | ESCAPE · PCN subset | CD-L1 (×1000): 13.58 -> 14.80 | Hurt |
| Replace Ball Query anchor refinement with clustering at threshold 0.5 (ablation) | ESCAPE · PCN subset | CD-L1 (×1000): 13.58 -> 15.73 | Hurt |
Surprising findings
- Models with better canonical-input results (AdaPoinTr, AnchorFormer) perform worst under rotated inputs on PCN, which the authors attribute to overfitting the dataset.
- SCARP fails to estimate the rotation of the partial cloud accurately even for unrotated inputs.
Limitations
- Relies on canonicalization (ConDor) for baselines, and comparisons depend on that choice; PCA alignment is only in the supplementary.
- Theoretical guarantees (constant error bounds, uniqueness) are sketched and rely on anchor points being in general position.
- Real-world evaluation on OmniObject uses only seven categories and median metrics, with no ground-truth-based full benchmark for KITTI.
Experimental setup
Datasets: PCN KITTI OmniObject3D
Benchmarks: PCN OmniObject3D KITTI Cars
Metrics: Chamfer Distance L1 (x1000) Chamfer Distance L2 MMD Fidelity MMID
Baselines: SnowflakeNet SeedFormer PoinTr AdaPoinTr AnchorFormer SCARP Vector Neurons
Builds on: AdaPoinTr DGCNN Chamfer Distance
Closest papers by meaning
- Learning Generalizable Shape Completion with SIM(3) Equivariance (NeurIPS 2025 · similarity 0.88)
- PCDreamer: Point Cloud Completion Through Multi-view Diffusion Priors (CVPR 2025 · similarity 0.85)
- Training-free Spatially Grounded Geometric Shape Encoding (NeurIPS 2026 · similarity 0.85)
- FSC: Few-point Shape Completion (CVPR 2024 · similarity 0.84)
- GeoComplete: Geometry-Aware Diffusion for Reference-Driven Image Completion (NeurIPS 2025 · similarity 0.84)
- SIEVE: Overcoming Topological Obstruction in Equivariant Self-Supervised Learning (NeurIPS 2026 · similarity 0.84)
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