# Leveraging 3D Geometric Priors in 2D Rotation Symmetry Detection

arXiv: https://arxiv.org/abs/2503.20235 · HTML: https://mlsanity.com/paper/2503.20235/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 35 references that are in the map.
- First posted on arXiv 26 Mar 2025.

## Builds on (most cited first, 17 of 17)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Deformable DETR: Deformable Transformers for End-to-End Object Detection](https://mlsanity.com/paper/2010.04159/) (2020)
- [BEVFormer: Learning Bird's-Eye-View Representation from Multi-Camera Images via Spatiotemporal Transformers](https://mlsanity.com/paper/2203.17270/) (2022)
- [Lift, Splat, Shoot: Encoding Images From Arbitrary Camera Rigs by Implicitly Unprojecting to 3D](https://mlsanity.com/paper/2008.05711/) (2020)
- [BEVDet: High-performance Multi-camera 3D Object Detection in Bird-Eye-View](https://mlsanity.com/paper/2112.11790/) (2021)
- [DETR3D: 3D Object Detection from Multi-view Images via 3D-to-2D Queries](https://mlsanity.com/paper/2110.06922/) (2021)
- [BEVDepth: Acquisition of Reliable Depth for Multi-view 3D Object Detection](https://mlsanity.com/paper/2206.10092/) (2022)
- [PETR: Position Embedding Transformation for Multi-View 3D Object Detection](https://mlsanity.com/paper/2203.05625/) (2022)
- [DN-DETR: Accelerate DETR Training by Introducing Query DeNoising](https://mlsanity.com/paper/2203.01305/) (2022)
- [Conditional DETR for Fast Training Convergence](https://mlsanity.com/paper/2108.06152/) (2021)
- [M2BEV: Multi-Camera Joint 3D Detection and Segmentation with Unified Birds-Eye View Representation](https://mlsanity.com/paper/2204.05088/) (2022)
- [SOLQ: Segmenting Objects by Learning Queries](https://mlsanity.com/paper/2106.02351/) (2021)
- [Beyond Planar Symmetry: Modeling human perception of reflection and rotation symmetries in the wild](https://mlsanity.com/paper/1704.03568/) (2017)
- [Reflection and Rotation Symmetry Detection via Equivariant Learning](https://mlsanity.com/paper/2203.16787/) (2022)
- [Parametric Depth Based Feature Representation Learning for Object Detection and Segmentation in Bird's Eye View](https://mlsanity.com/paper/2307.04106/) (2023)

## Built on by (most cited first, 3 of 3)

- [Axis-level Symmetry Detection with Group-Equivariant Representation](https://mlsanity.com/paper/2508.10740/) (2025)
- [CLIPSym: Delving into Symmetry Detection with CLIP](https://mlsanity.com/paper/2508.14197/) (2025)
- [ARD-REFSM: Enhancing Reflection Symmetry Detection with Asymmetric Denoising and Rotation Equivariance](https://mlsanity.com/paper/2607.27927/) (2026)

## Abstract (arXiv)

Symmetry plays a vital role in understanding structural patterns, aiding object recognition and scene interpretation. This paper focuses on rotation symmetry, where objects remain unchanged when rotated around a central axis, requiring detection of rotation centers and supporting vertices. Traditional methods relied on hand-crafted feature matching, while recent segmentation models based on convolutional neural networks detect rotation centers but struggle with 3D geometric consistency due to viewpoint distortions. To overcome this, we propose a model that directly predicts rotation centers and vertices in 3D space and projects the results back to 2D while preserving structural integrity. By incorporating a vertex reconstruction stage enforcing 3D geometric priors -- such as equal side lengths and interior angles -- our model enhances robustness and accuracy. Experiments on the DENDI dataset show superior performance in rotation axis detection and validate the impact of 3D priors through ablation studies.