# PRS-Net: Planar Reflective Symmetry Detection Net for 3D Models

arXiv: https://arxiv.org/abs/1910.06511 · HTML: https://mlsanity.com/paper/1910.06511/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Oct 2019.

## Built on by (most cited first, 20 of 20)

- [Robust Symmetry Detection via Riemannian Langevin Dynamics](https://mlsanity.com/paper/2410.02786/) (2024)
- [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)
- [Learning Proximal Operators to Discover Multiple Optima](https://mlsanity.com/paper/2201.11945/) (2022)
- [A dataset-free approach for self-supervised learning of 3D reflectional symmetries](https://mlsanity.com/paper/2503.02660/) (2025)
- [Black-Box Test-Time Shape REFINEment for Single View 3D Reconstruction](https://mlsanity.com/paper/2108.09911/) (2021)
- [High-Fidelity Point Cloud Completion with Low-Resolution Recovery and Noise-Aware Upsampling](https://mlsanity.com/paper/2112.11271/) (2021)
- [Robust Extrinsic Symmetry Estimation in 3D Point Clouds](https://mlsanity.com/paper/2109.09927/) (2021)
- [GIQ: Benchmarking 3D Geometric Reasoning of Vision Foundation Models with Simulated and Real Polyhedra](https://mlsanity.com/paper/2506.08194/) (2025)
- [Breaking the Symmetry: Resolving Symmetry Ambiguities in Equivariant Neural Networks](https://mlsanity.com/paper/2210.16646/) (2022)
- [Partial Symmetry Detection for 3D Geometry using Contrastive Learning with Geodesic Point Cloud Patches](https://mlsanity.com/paper/2312.08230/) (2023)
- [Quartet of Diffusions: Structure-Aware Point Cloud Generation through Part and Symmetry Guidance](https://mlsanity.com/paper/2601.20425/) (2026)
- [Recurrently Estimating Reflective Symmetry Planes from Partial Pointclouds](https://mlsanity.com/paper/2106.16129/) (2021)
- [Automatic Skull Reconstruction by Deep Learnable Symmetry Enforcement](https://mlsanity.com/paper/2411.17342/) (2024)
- [Training-free zero-shot 3D symmetry detection with visual features back-projected to geometry](https://mlsanity.com/paper/2505.24162/) (2025)
- [Symmetria: A Synthetic Dataset for Learning in Point Clouds](https://mlsanity.com/paper/2510.23414/) (2025)
- [SymGS : Leveraging Local Symmetries for 3D Gaussian Splatting Compression](https://mlsanity.com/paper/2511.13264/) (2025)
- [Global Symmetry and Orthogonal Transformations from Geometrical Moment n-tuples](https://mlsanity.com/paper/2602.07736/) (2026)
- [ArchSym: Detecting 3D-Grounded Architectural Symmetries in the Wild](https://mlsanity.com/paper/2604.22202/) (2026)
- [ARD-REFSM: Enhancing Reflection Symmetry Detection with Asymmetric Denoising and Rotation Equivariance](https://mlsanity.com/paper/2607.27927/) (2026)

## Abstract (arXiv)

In geometry processing, symmetry is a universal type of high-level structural information of 3D models and benefits many geometry processing tasks including shape segmentation, alignment, matching, and completion. Thus it is an important problem to analyze various symmetry forms of 3D shapes. Planar reflective symmetry is the most fundamental one. Traditional methods based on spatial sampling can be time-consuming and may not be able to identify all the symmetry planes. In this paper, we present a novel learning framework to automatically discover global planar reflective symmetry of a 3D shape. Our framework trains an unsupervised 3D convolutional neural network to extract global model features and then outputs possible global symmetry parameters, where input shapes are represented using voxels. We introduce a dedicated symmetry distance loss along with a regularization loss to avoid generating duplicated symmetry planes. Our network can also identify generalized cylinders by predicting their rotation axes. We further provide a method to remove invalid and duplicated planes and axes. We demonstrate that our method is able to produce reliable and accurate results. Our neural network based method is hundreds of times faster than the state-of-the-art methods, which are based on sampling. Our method is also robust even with noisy or incomplete input surfaces.