Research map / Point clouds / Shape and surface completion
Learning SO(3)-Invariant Semantic Correspondence via Local Shape Transform
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Proposes RIST, a self-supervised SO(3)-invariant 3D dense correspondence learner that uses dynamic point-wise local shape transforms over SO(3)-equivariant VN-DGCNN features, trained by self- and cross-reconstruction.
Problem
Establishing dense semantic correspondences between 3D shapes of the same category when point clouds are arbitrarily rotated; existing self-supervised methods assume aligned inputs and degrade under rotation.
Approach
Dynamically predict input-dependent, per-point local shape transforms from SO(3)-invariant features that map the SO(3)-equivariant global shape descriptor to local shape descriptors fed to an SO(3)-equivariant decoder; train via self- and cross-reconstruction so semantically corresponding points get similar local descriptors.
Key results
- On ShapeNetPart part label transfer with rotations during training, RIST averages 57.8% IoU versus 32.4% for CPAE.
- On ScanObjectNN chair part label transfer, RIST reaches 39.6% IoU without rotation augmentation versus 24.4% for CPAE.
- On KeypointNet keypoint transfer, RIST outperforms baselines across all 12 categories and thresholds, by up to 10x on certain classes and thresholds.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use RIST instead of DPC | 3D part label transfer · ShapeNetPart, w/o rotations | average IoU (%): 32.2 -> 57.6 | Helped |
| Use RIST instead of DPC | 3D part label transfer · ShapeNetPart, w/ rotations | average IoU (%): 34.0 -> 57.8 | Helped |
| Use RIST instead of CPAE | 3D part label transfer · ScanObjectNN chair, w/o rotations | average IoU (%): 24.4 -> 39.6 | Helped |
| Use RIST instead of FoldingNet | 3D part label transfer · ScanObjectNN chair, w/ rotations | average IoU (%): 23.3 -> 37.9 | Helped |
| Use RIST rather than previous approaches | 3D semantic keypoint transfer · KeypointNet, 12 categories | PCK: up to 10⇥ | Helped |
| Remove self-reconstruction loss (ablation) | RIST · KeypointNet motorcycle | PCK | Hurt |
| Remove cross-reconstruction loss (ablation) | RIST · KeypointNet motorcycle | PCK | Hurt |
| Replace the equivariant decoder with an SO(3)-variant decoder (ablation) | RIST · KeypointNet motorcycle | PCK | Hurt |
| Replace local shape transforms with UV coordinates (ablation) | RIST · KeypointNet motorcycle | PCK | Hurt |
| Replace point-wise local features with global features for encoding (ablation) | RIST · KeypointNet motorcycle | PCK | Mixed |
Surprising findings
- Existing methods' performance degrades significantly under arbitrary rotations, and the Bathtub and Table classes show only small margins, which the authors attribute to rotational symmetry.
Limitations
- Performance on classes with prevalent rotational symmetry (e.g., Bathtub, Table) is only marginally better than baselines.
- Robustness under common corruptions is not addressed.
Experimental setup
Datasets: ShapeNetPart KeypointNet ScanObjectNN
Benchmarks: ShapeNetPart ScanObjectNN KeypointNet
Metrics: average instance-wise IoU PCK
Baselines: CPAE AtlasNetV2 FoldingNet DPC
Builds on: VNN (vector neurons) CPAE DGCNN FoldingNet
Closest papers by meaning
- RINO: Rotation-Invariant Non-Rigid Correspondences (CVPR 2026 · similarity 0.90)
- Learning Shape-Independent Transformation via Spherical Representations for Category-Level Object Pose Estimation (ICLR 2025 · similarity 0.87)
- Local-consistent Transformation Learning for Rotation-invariant Point Cloud Analysis (CVPR 2024 · similarity 0.86)
- Improving Semantic Correspondence with Viewpoint-Guided Spherical Maps (CVPR 2024 · similarity 0.86)
- SIEVE: Overcoming Topological Obstruction in Equivariant Self-Supervised Learning (NeurIPS 2026 · 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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