# NeRD++: Improved 3D-mirror symmetry learning from a single image

arXiv: https://arxiv.org/abs/2112.12579 · HTML: https://mlsanity.com/paper/2112.12579/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 26 references that are in the map.
- First posted on arXiv 23 Dec 2021.

## Builds on (most cited first, 16 of 16)

- [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)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [Normalized Object Coordinate Space for Category-Level 6D Object Pose and Size Estimation](https://mlsanity.com/paper/1901.02970/) (2019)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [Pix3D: Dataset and Methods for Single-Image 3D Shape Modeling](https://mlsanity.com/paper/1804.04610/) (2018)
- [Unsupervised Learning of Probably Symmetric Deformable 3D Objects from Images in the Wild](https://mlsanity.com/paper/1911.11130/) (2019)
- [Morphing and Sampling Network for Dense Point Cloud Completion](https://mlsanity.com/paper/1912.00280/) (2019)
- [Deep Hough-Transform Line Priors](https://mlsanity.com/paper/2007.09493/) (2020)
- [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)
- [Front2Back: Single View 3D Shape Reconstruction via Front to Back Prediction](https://mlsanity.com/paper/1912.10589/) (2019)
- [Learning to Discover Reflection Symmetry via Polar Matching Convolution](https://mlsanity.com/paper/2108.12952/) (2021)

## Built on by (most cited first, 4 of 4)

- [VoteFlow: Enforcing Local Rigidity in Self-Supervised Scene Flow](https://mlsanity.com/paper/2503.22328/) (2025)
- [Symmetry Strikes Back: From Single-Image Symmetry Detection to 3D Generation](https://mlsanity.com/paper/2411.17763/) (2024)
- [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)

Many objects are naturally symmetric, and this symmetry can be exploited to infer unseen 3D properties from a single 2D image. Recently, NeRD is proposed for accurate 3D mirror plane estimation from a single image. Despite the unprecedented accuracy, it relies on large annotated datasets for training and suffers from slow inference. Here we aim to improve its data and compute efficiency. We do away with the computationally expensive 4D feature volumes and instead explicitly compute the feature correlation of the pixel correspondences across depth, thus creating a compact 3D volume. We also design multi-stage spherical convolutions to identify the optimal mirror plane on the hemisphere, whose inductive bias offers gains in data-efficiency. Experiments on both synthetic and real-world datasets show the benefit of our proposed changes for improved data efficiency and inference speed.