# NeRD: Neural 3D Reflection Symmetry Detector

arXiv: https://arxiv.org/abs/2105.03211 · HTML: https://mlsanity.com/paper/2105.03211/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 48 references that are in the map.
- First posted on arXiv 19 Apr 2021.

## Builds on (most cited first, 30 of 30)

- [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)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [Stacked Hourglass Networks for Human Pose Estimation](https://mlsanity.com/paper/1603.06937/) (2016)
- [Deep Ordinal Regression Network for Monocular Depth Estimation](https://mlsanity.com/paper/1806.02446/) (2018)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [Frustum PointNets for 3D Object Detection from RGB-D Data](https://mlsanity.com/paper/1711.08488/) (2017)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Normalized Object Coordinate Space for Category-Level 6D Object Pose and Size Estimation](https://mlsanity.com/paper/1901.02970/) (2019)
- [Pyramid Stereo Matching Network](https://mlsanity.com/paper/1803.08669/) (2018)
- [Soft Rasterizer: A Differentiable Renderer for Image-based 3D Reasoning](https://mlsanity.com/paper/1904.01786/) (2019)
- [End-to-End Learning of Geometry and Context for Deep Stereo Regression](https://mlsanity.com/paper/1703.04309/) (2017)
- [GeoNet: Unsupervised Learning of Dense Depth, Optical Flow and Camera Pose](https://mlsanity.com/paper/1803.02276/) (2018)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [3D Bounding Box Estimation Using Deep Learning and Geometry](https://mlsanity.com/paper/1612.00496/) (2016)
- [What Do Single-view 3D Reconstruction Networks Learn?](https://mlsanity.com/paper/1905.03678/) (2019)
- [BB8: A Scalable, Accurate, Robust to Partial Occlusion Method for Predicting the 3D Poses of Challenging Objects without Using Depth](https://mlsanity.com/paper/1703.10896/) (2017)
- [Pix3D: Dataset and Methods for Single-Image 3D Shape Modeling](https://mlsanity.com/paper/1804.04610/) (2018)
- [Real-Time Seamless Single Shot 6D Object Pose Prediction](https://mlsanity.com/paper/1711.08848/) (2017)
- [Learning a Multi-View Stereo Machine](https://mlsanity.com/paper/1708.05375/) (2017)
- [Unsupervised Learning of Probably Symmetric Deformable 3D Objects from Images in the Wild](https://mlsanity.com/paper/1911.11130/) (2019)
- [High Quality Monocular Depth Estimation via Transfer Learning](https://mlsanity.com/paper/1812.11941/) (2018)
- [Deep Sliding Shapes for Amodal 3D Object Detection in RGB-D Images](https://mlsanity.com/paper/1511.02300/) (2015)
- [Unsupervised Learning of Shape and Pose with Differentiable Point Clouds](https://mlsanity.com/paper/1810.09381/) (2018)
- [Portrait Shadow Manipulation](https://mlsanity.com/paper/2005.08925/) (2020)
- [NeurVPS: Neural Vanishing Point Scanning via Conic Convolution](https://mlsanity.com/paper/1910.06316/) (2019)
- [Ladybird: Quasi-Monte Carlo Sampling for Deep Implicit Field Based 3D Reconstruction with Symmetry](https://mlsanity.com/paper/2007.13393/) (2020)
- [Beyond Planar Symmetry: Modeling human perception of reflection and rotation symmetries in the wild](https://mlsanity.com/paper/1704.03568/) (2017)
- [Front2Back: Single View 3D Shape Reconstruction via Front to Back Prediction](https://mlsanity.com/paper/1912.10589/) (2019)

## Built on by (most cited first, 18 of 18)

- [SymmCompletion: High-Fidelity and High-Consistency Point Cloud Completion with Symmetry Guidance](https://mlsanity.com/paper/2503.18007/) (2025)
- [Robust Symmetry Detection via Riemannian Langevin Dynamics](https://mlsanity.com/paper/2410.02786/) (2024)
- [SymmNeRF: Learning to Explore Symmetry Prior for Single-View View Synthesis](https://mlsanity.com/paper/2209.14819/) (2022)
- [SNeS: Learning Probably Symmetric Neural Surfaces from Incomplete Data](https://mlsanity.com/paper/2206.06340/) (2022)
- [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)
- [Black-Box Test-Time Shape REFINEment for Single View 3D Reconstruction](https://mlsanity.com/paper/2108.09911/) (2021)
- [Robust Extrinsic Symmetry Estimation in 3D Point Clouds](https://mlsanity.com/paper/2109.09927/) (2021)
- [SPA-VAE: Similar-Parts-Assignment for Unsupervised 3D Point Cloud Generation](https://mlsanity.com/paper/2203.07825/) (2022)
- [Symmetry Perception by Deep Networks: Inadequacy of Feed-Forward Architectures and Improvements with Recurrent Connections](https://mlsanity.com/paper/2112.04162/) (2021)
- [Quartet of Diffusions: Structure-Aware Point Cloud Generation through Part and Symmetry Guidance](https://mlsanity.com/paper/2601.20425/) (2026)
- [Inferring Implicit 3D Representations from Human Figures on Pictorial Maps](https://mlsanity.com/paper/2209.02385/) (2022)
- [Automatic Skull Reconstruction by Deep Learnable Symmetry Enforcement](https://mlsanity.com/paper/2411.17342/) (2024)
- [Symmetry Matters: Auditing and Symmetrizing 3D Generative Models](https://mlsanity.com/paper/2512.18953/) (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)

Recent advances have shown that symmetry, a structural prior that most objects exhibit, can support a variety of single-view 3D understanding tasks. However, detecting 3D symmetry from an image remains a challenging task. Previous works either assume that the symmetry is given or detect the symmetry with a heuristic-based method. In this paper, we present NeRD, a Neural 3D Reflection Symmetry Detector, which combines the strength of learning-based recognition and geometry-based reconstruction to accurately recover the normal direction of objects' mirror planes. Specifically, we first enumerate the symmetry planes with a coarse-to-fine strategy and then find the best ones by building 3D cost volumes to examine the intra-image pixel correspondence from the symmetry. Our experiments show that the symmetry planes detected with our method are significantly more accurate than the planes from direct CNN regression on both synthetic and real-world datasets. We also demonstrate that the detected symmetry can be used to improve the performance of downstream tasks such as pose estimation and depth map regression. The code of this paper has been made public at https://github.com/zhou13/nerd.