# ARD-REFSM: Enhancing Reflection Symmetry Detection with Asymmetric Denoising and Rotation Equivariance

arXiv: https://arxiv.org/abs/2607.27927 · HTML: https://mlsanity.com/paper/2607.27927/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 56 references that are in the map.
- First posted on arXiv 30 Jul 2026.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [General E(2)-Equivariant Steerable CNNs](https://mlsanity.com/paper/1911.08251/) (2019)
- [ReDet: A Rotation-equivariant Detector for Aerial Object Detection](https://mlsanity.com/paper/2103.07733/) (2021)
- [PRS-Net: Planar Reflective Symmetry Detection Net for 3D Models](https://mlsanity.com/paper/1910.06511/) (2019)
- [NeRD: Neural 3D Reflection Symmetry Detector](https://mlsanity.com/paper/2105.03211/) (2021)
- [Beyond Planar Symmetry: Modeling human perception of reflection and rotation symmetries in the wild](https://mlsanity.com/paper/1704.03568/) (2017)
- [Robust Symmetry Detection via Riemannian Langevin Dynamics](https://mlsanity.com/paper/2410.02786/) (2024)
- [Reflection and Rotation Symmetry Detection via Equivariant Learning](https://mlsanity.com/paper/2203.16787/) (2022)
- [Learning to Discover Reflection Symmetry via Polar Matching Convolution](https://mlsanity.com/paper/2108.12952/) (2021)
- [A convolutional approach to reflection symmetry](https://mlsanity.com/paper/1609.05257/) (2016)
- [SRN: Side-output Residual Network for Object Symmetry Detection in the Wild](https://mlsanity.com/paper/1703.02243/) (2017)
- [Symmetry Strikes Back: From Single-Image Symmetry Detection to 3D Generation](https://mlsanity.com/paper/2411.17763/) (2024)
- [NeRD++: Improved 3D-mirror symmetry learning from a single image](https://mlsanity.com/paper/2112.12579/) (2021)
- [Leveraging 3D Geometric Priors in 2D Rotation Symmetry Detection](https://mlsanity.com/paper/2503.20235/) (2025)
- [Multiple Reflection Symmetry Detection via Linear-Directional Kernel Density Estimation](https://mlsanity.com/paper/1704.06392/) (2017)

## Abstract (arXiv)

Reflection symmetry detection remains challenging due to interference from asymmetric regions and arbitrary orientations of symmetric patterns. Asymmetric regions introduce background clutter that disrupts symmetric pattern matching, whereas conventional convolutional neural networks lack rotation equivariance, leading to inconsistent feature representations under rotational transformations. To address these issues, we propose an Asymmetric Region Denoising (ARD) module and a Rotation Equivariant Feature Similarity Matching (REFSM) module. The ARD module suppresses asymmetric interference to refine symmetric patterns, while the REFSM module enhances rotation equivariance through feature similarity matching between original and rotated images. Specifically, our dual-input REFSM framework leverages rotation loss to maximize consistency between the score maps of original and rotated images, thereby enabling precise prediction of rotation-equivariant symmetry axes. Furthermore, we introduce GMSYM, a new benchmark dataset that categorizes images into diverse scenarios and incorporates various interferences to address the limitations of existing reflection symmetry detection benchmarks. Extensive experiments on four standard datasets (DENDI, NYU, LDRS, SDRW) and our proposed GMSYM dataset demonstrate that our method achieves state-of-the-art performance in both accuracy and robustness.