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Symmetry-Robust 3D Orientation Estimation
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Proposes a two-stage 3D orientation pipeline (octahedral-quotient regression followed by a 24-way flip classifier with conformal adaptive prediction sets) trained on all of ShapeNet, reaching SOTA up-axis accuracy.
Problem
Estimating a 3D shape's full orientation (side, up, front axes) is ill-posed for rotationally symmetric shapes, since L2 regression collapses to Euclidean means and classification over dense rotation grids fails.
Approach
Split orientation into a continuous quotient regression that recovers orientation up to octahedral symmetries, and a discrete 24-class flipper that resolves the remaining octahedral ambiguity; add conformal adaptive prediction sets for ambiguous cases.
Key results
- Up-axis accuracy on ShapeNet validation: 89.2% with TTA vs 69.5% for Upright-Net; on ModelNet40 77.7% vs 62.3%.
- Full-orientation mean chamfer distance 0.00856 (TTA) vs 0.05481 for Upright-Net-Oracle, an 84% reduction.
- With adaptive prediction sets (coverage 0.3), median set size is 2 and the minimum chamfer distance in the set is 4x lower than without APS.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add test-time augmentation (ablation) | Ours · Shapenet | accuracy: 85.3 % -> 89.2 % | Helped |
| add test-time augmentation (ablation) | Ours · ModelNet40 | accuracy: 72.3 % -> 77.7 % | Helped |
| use the two-stage orientation pipeline instead of Upright-Net | up-axis estimation · Shapenet | accuracy: 69.5 % -> 89.2 % | Helped |
| use the two-stage orientation pipeline instead of Upright-Net | up-axis estimation · ModelNet40 | accuracy: 62.3 % -> 77.7 % | Helped |
| add test-time augmentation (ablation) | Ours · Shapenet validation | mean chamfer distance: 0.01107 ± 0.04342 -> 0.00856 ± 0.0396 | Helped |
| add adaptive prediction sets (ablation) | Ours · Shapenet validation | mean chamfer distance: 0.00856 ± 0.0396 -> 0.00208 ± 0.01407 | Helped |
| use the two-stage pipeline instead of Upright-Net-Oracle | full-orientation estimation · Shapenet validation | mean chamfer distance: 0.05481 ± 0.13016 -> 0.00856 ± 0.0396 | Helped |
Surprising findings
- L2 regression of orientations provably degenerates to Euclidean means for rotationally symmetric shapes, producing a submanifold of solutions even for a single symmetry.
Limitations
- Flipper fails more often on out-of-distribution data such as ModelNet40 and Objaverse, with 90 and 180 degree errors.
- Quotient orienter fails on small subsets of rotations, requiring test-time augmentation.
- Ground-truth orientations are human-determined and may be ambiguous, so evaluation relies on shape-level chamfer distance.
Experimental setup
Datasets: ShapeNet ModelNet40 Objaverse
Benchmarks: ShapeNet validation ModelNet40
Metrics: up-axis accuracy at 10 degree threshold mean symmetric chamfer distance adaptive prediction set size
Baselines: Upright-Net Upright-Net-Oracle Upright-Net-Random
Builds on: DGCNN adaptive prediction sets Upright-Net
Closest papers by meaning
- Leveraging 3D Geometric Priors in 2D Rotation Symmetry Detection (CVPR 2025 · similarity 0.88)
- Orient Anything V2: Unifying Orientation and Rotation Understanding (NeurIPS 2025 · similarity 0.88)
- Orient Anything: Learning Robust Object Orientation Estimation from Rendering 3D Models (ICML 2025 · similarity 0.87)
- Consistent Normal Orientation for 3D Point Clouds via Least Squares on Delaunay Graph (CVPR 2025 · similarity 0.86)
- Orientation Matters: Making 3D Generative Models Orientation-Aligned (NeurIPS 2025 · similarity 0.85)
- Symmetry Strikes Back: From Single-Image Symmetry Detection to 3D Generation (CVPR 2025 · similarity 0.84)
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