# Beyond Planar Symmetry: Modeling human perception of reflection and rotation symmetries in the wild

arXiv: https://arxiv.org/abs/1704.03568 · HTML: https://mlsanity.com/paper/1704.03568/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Apr 2017.

## Built on by (most cited first, 17 of 17)

- [NeRD: Neural 3D Reflection Symmetry Detector](https://mlsanity.com/paper/2105.03211/) (2021)
- [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)
- [Symmetry-Aware Transformer-based Mirror Detection](https://mlsanity.com/paper/2207.06332/) (2022)
- [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)
- [GIQ: Benchmarking 3D Geometric Reasoning of Vision Foundation Models with Simulated and Real Polyhedra](https://mlsanity.com/paper/2506.08194/) (2025)
- [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)
- [Symmetry Perception by Deep Networks: Inadequacy of Feed-Forward Architectures and Improvements with Recurrent Connections](https://mlsanity.com/paper/2112.04162/) (2021)
- [Recurrently Estimating Reflective Symmetry Planes from Partial Pointclouds](https://mlsanity.com/paper/2106.16129/) (2021)
- [Using Machine Learning to Detect Rotational Symmetries from Reflectional Symmetries in 2D Images](https://mlsanity.com/paper/2201.06594/) (2022)
- [EscherNet 101](https://mlsanity.com/paper/2303.04208/) (2023)
- [Symmetric Perception and Ordinal Regression for Detecting Scoliosis Natural Image](https://mlsanity.com/paper/2411.15799/) (2024)
- [ArchSym: Detecting 3D-Grounded Architectural Symmetries in the Wild](https://mlsanity.com/paper/2604.22202/) (2026)
- [Water Reflection Detection Using Symmetric Attention](https://mlsanity.com/paper/2607.10749/) (2026)
- [ARD-REFSM: Enhancing Reflection Symmetry Detection with Asymmetric Denoising and Rotation Equivariance](https://mlsanity.com/paper/2607.27927/) (2026)

## Abstract (arXiv)

Humans take advantage of real world symmetries for various tasks, yet capturing their superb symmetry perception mechanism with a computational model remains elusive. Motivated by a new study demonstrating the extremely high inter-person accuracy of human perceived symmetries in the wild, we have constructed the first deep-learning neural network for reflection and rotation symmetry detection (Sym-NET), trained on photos from MS-COCO (Microsoft-Common Object in COntext) dataset with nearly 11K consistent symmetry-labels from more than 400 human observers. We employ novel methods to convert discrete human labels into symmetry heatmaps, capture symmetry densely in an image and quantitatively evaluate Sym-NET against multiple existing computer vision algorithms. On CVPR 2013 symmetry competition testsets and unseen MS-COCO photos, Sym-NET significantly outperforms all other competitors. Beyond mathematically well-defined symmetries on a plane, Sym-NET demonstrates abilities to identify viewpoint-varied 3D symmetries, partially occluded symmetrical objects, and symmetries at a semantic level.