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Leveraging 3D Geometric Priors in 2D Rotation Symmetry Detection
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Proposes a DETR-style detector that predicts 3D rotation centers and vertices with a vertex reconstruction stage enforcing 3D symmetry priors, projecting results to 2D for rotation symmetry detection.
Problem
Detecting 2D rotation symmetry (rotation centers, supporting vertices, symmetry group) from images, where 2D ground truth is labeled from a 3D perspective and 2D CNN segmentation models struggle with 3D geometric consistency under viewpoint distortion.
Approach
Camera queries and camera cross-attention lift image features into 3D camera coordinates; the head predicts a center, seed vertex and axis, and vertices are generated by Rodrigues rotation of the seed around the axis according to the predicted group order, then projected to 2D. Set-based bipartite matching trains centers and vertices in two steps.
Key results
- Vertex detection mAP improves from 24.7 (2D baseline) and 23.5 (3D baseline) to 30.6 with vertex reconstruction on DENDI.
- Rotation symmetry detection max F1 of 33.2 vs. 22.5 for EquiSym on DENDI.
- Rotation center AP mean of 31.3 across groups on DENDI.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace EquiSym segmentation with detection-based prediction | Ours · DENDI rotation symmetry detection | maximum F1-score: 22.5 -> 33.2 | Helped |
| add 3D query/prediction to the 2D baseline (ablation) | rotation vertex detector · DENDI rotation vertex detection | mAP: 24.7 -> 23.5 | Hurt |
| add vertex reconstruction with symmetry-aware 3D geometric priors (ablation) | 3D baseline · DENDI rotation vertex detection | mAP: 23.5 -> 30.6 | Helped |
Surprising findings
- The naive 3D baseline (23.5 mAP) slightly underperforms the 2D baseline (24.7), suggesting 3D lifting alone without geometric constraints hurts performance.
Limitations
- Struggles to estimate rotation axis under severe viewpoint variations.
- Assumes known/fixed camera intrinsics since DENDI lacks them; focal length fixed to 1000.
- Low AP on C3 and C6 groups, possibly due to few test samples.
Experimental setup
Datasets: DENDI
Benchmarks: DENDI
Metrics: average precision max F1-score
Baselines: EquiSym 2D baseline 3D baseline
Builds on: DETR Deformable DETR BEVFormer EquiSym
Closest papers by meaning
- Symmetry-Robust 3D Orientation Estimation (ICML 2025 · similarity 0.88)
- Symmetry Strikes Back: From Single-Image Symmetry Detection to 3D Generation (CVPR 2025 · similarity 0.87)
- R2Det: Exploring Relaxed Rotation Equivariance in 2D Object Detection (ICLR 2025 · similarity 0.87)
- Orient Anything V2: Unifying Orientation and Rotation Understanding (NeurIPS 2025 · similarity 0.86)
- GIQ: Benchmarking 3D Geometric Reasoning of Vision Foundation Models with Simulated and Real Polyhedra (ICLR 2026 · similarity 0.85)
- Registration is a Powerful Rotation-Invariance Learner for 3D Anomaly Detection (NeurIPS 2025 · similarity 0.85)
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