# A convolutional approach to reflection symmetry

arXiv: https://arxiv.org/abs/1609.05257 · HTML: https://mlsanity.com/paper/1609.05257/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2016.

## Built on by (most cited first, 10 of 10)

- [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)
- [Semantic Line Detection Using Mirror Attention and Comparative Ranking and Matching](https://mlsanity.com/paper/2203.15285/) (2022)
- [CLIPSym: Delving into Symmetry Detection with CLIP](https://mlsanity.com/paper/2508.14197/) (2025)
- [Symmetry Perception by Deep Networks: Inadequacy of Feed-Forward Architectures and Improvements with Recurrent Connections](https://mlsanity.com/paper/2112.04162/) (2021)
- [Semantic Line Combination Detector](https://mlsanity.com/paper/2404.18399/) (2024)
- [Recurrently Estimating Reflective Symmetry Planes from Partial Pointclouds](https://mlsanity.com/paper/2106.16129/) (2021)
- [Optimal Transport with Cyclic Symmetry](https://mlsanity.com/paper/2311.13147/) (2023)
- [Classical Versus Deep Mirror-Symmetry Scoring: A Benchmark of Thirteen Methods](https://mlsanity.com/paper/2607.08379/) (2026)
- [ARD-REFSM: Enhancing Reflection Symmetry Detection with Asymmetric Denoising and Rotation Equivariance](https://mlsanity.com/paper/2607.27927/) (2026)

## Abstract (arXiv)

We present a convolutional approach to reflection symmetry detection in 2D. Our model, built on the products of complex-valued wavelet convolutions, simplifies previous edge-based pairwise methods. Being parameter-centered, as opposed to feature-centered, it has certain computational advantages when the object sizes are known a priori, as demonstrated in an ellipse detection application. The method outperforms the best-performing algorithm on the CVPR 2013 Symmetry Detection Competition Database in the single-symmetry case. Code and a new database for 2D symmetry detection is available.