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PolyhedronNet: Representation Learning for Polyhedra with Surface-attributed Graph
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Proposes PolyhedronNet, which models a 3D polyhedron as a surface-attributed graph and aggregates local rigid two-hop-path representations with a hierarchical GNN (PolyhedronGNN) for rotation- and translation-invariant polyhedron classification and retrieval.
Problem
Learning vector representations of 3D polyhedral objects that capture vertices, edges, faces, face attributes and geometry while being rotation and translation invariant, for classification and retrieval.
Approach
Represent a polyhedron as a surface-attributed graph with face-hyperedges, encode each two-hop path with a rigid five-tuple of distances, angle, dihedral angle and face index, and aggregate these with a heterogeneous intra-face/inter-face message-passing GNN.
Key results
- On MNIST-C classification, PolyhedronNet reaches accuracy 0.858 and AUC 0.985 versus 0.435 accuracy for PolygonGNN, the best baseline.
- On Building classification, PolyhedronNet reaches AUC 1.000 and accuracy 0.980.
- On ShapeNet-P classification, accuracy is 0.627 and AUC 0.936; on ModelNet-P accuracy is 0.435 and AUC 0.824.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use PolyhedronNet rather than the strongest listed baseline | PolyhedronNet · MNIST-C classification | Acc: 0.435 -> 0.858 | Helped |
| use PolyhedronNet rather than the strongest listed baseline | PolyhedronNet · Building classification | Acc: 0.973 -> 0.980 | Helped |
| use PolyhedronNet rather than the strongest listed baseline | PolyhedronNet · ShapeNet-P classification | Acc: 0.573 -> 0.627 | Helped |
| use PolyhedronNet rather than the strongest listed baseline | PolyhedronNet · ModelNet-P classification | Acc: 0.430 -> 0.435 | Helped |
| use PolyhedronNet rather than the strongest listed baseline | PolyhedronNet · MNIST-C retrieval | MAP: 0.696 -> 0.842 | Helped |
| use PolyhedronNet rather than the strongest listed baseline | PolyhedronNet · Building retrieval | MAP: 0.890 -> 0.923 | Helped |
| use PolyhedronNet rather than the strongest listed baseline | PolyhedronNet · ShapeNet-P retrieval | MAP: 0.476 -> 0.486 | Helped |
| use PolyhedronNet rather than the strongest listed baseline | PolyhedronNet · ModelNet-P retrieval | MAP: 0.415 -> 0.421 | Helped |
| add face attributes instead of masking them with zeroes (ablation) | PolyhedronNet · MNIST-C classification | Acc: 0.360 -> 0.858 | Helped |
| add face attributes instead of masking them with zeroes (ablation) | PolyhedronNet · ShapeNet-P classification | Acc: 0.578 -> 0.627 | Helped |
| add face attributes instead of masking them with zeroes (ablation) | PolyhedronNet · MNIST-C retrieval | MAP: 0.534 -> 0.842 | Helped |
| add face attributes instead of masking them with zeroes (ablation) | PolyhedronNet · ShapeNet-P retrieval | MAP: 0.482 -> 0.486 | Helped |
Surprising findings
- Competing polygon and sequence-based methods (NUFT-DDSL, ResNet1D, NUFT-IFFT, VeerCNN) perform near chance on ShapeNet-P and MNIST-C, showing the difficulty of rotated polyhedra.
- Removing face attributes drops MNIST-C classification accuracy from 0.858 to 0.360.
Limitations
- Datasets are small (1,303 to 13,742 samples) and ModelNet-P and ShapeNet-P accuracy remains modest (about 0.43 and 0.63).
- Face attributes are required for the largest gains; Building and ModelNet-P have no face attributes, so the advantage there depends on geometry alone.
Experimental setup
Datasets: MNIST-C Building ShapeNet-P ModelNet-P MNIST-P OpenStreetMap building dataset ShapeNetCore ModelNet40
Benchmarks: MNIST-C Building ShapeNet-P ModelNet-P
Metrics: Accuracy Weighted Precision Weighted F1 Weighted ROC AUC Precision Recall F1 MAP NDCG
Baselines: NUFT-DDSL ResNet1D NUFT-IFFT VeerCNN PolygonGNN HGT HAN LocoTrans RISurConv
Builds on: PolygonGNN PointNet
Closest papers by meaning
- GIQ: Benchmarking 3D Geometric Reasoning of Vision Foundation Models with Simulated and Real Polyhedra (ICLR 2026 · similarity 0.87)
- Unsupervised Learning of Intrinsic Structural Representation Points (CVPR 2020 · similarity 0.87)
- UV-Net: Learning From Boundary Representations (CVPR 2021 · similarity 0.86)
- 3DCoMPaT200: Language Grounded Large-Scale 3D Vision Dataset for Compositional Recognition (NeurIPS 2024 · similarity 0.85)
- PoNQ: a Neural QEM-based Mesh Representation (CVPR 2024 · similarity 0.85)
- Polyhedral Complex Derivation from Piecewise Trilinear Networks (NeurIPS 2024 · similarity 0.84)
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