# Robust Extrinsic Symmetry Estimation in 3D Point Clouds

arXiv: https://arxiv.org/abs/2109.09927 · HTML: https://mlsanity.com/paper/2109.09927/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 85 references that are in the map.
- First posted on arXiv 21 Sep 2021.

## Builds on (most cited first, 13 of 13)

- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Unsupervised Learning of Probably Symmetric Deformable 3D Objects from Images in the Wild](https://mlsanity.com/paper/1911.11130/) (2019)
- [EPOS: Estimating 6D Pose of Objects with Symmetries](https://mlsanity.com/paper/2004.00605/) (2020)
- [Manopt, a Matlab toolbox for optimization on manifolds](https://mlsanity.com/paper/1308.5200/) (2013)
- [ZoomOut: Spectral Upsampling for Efficient Shape Correspondence](https://mlsanity.com/paper/1904.07865/) (2019)
- [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)
- [MapTree: Recovering Multiple Solutions in the Space of Maps](https://mlsanity.com/paper/2006.02532/) (2020)
- [Learning to Discover Reflection Symmetry via Polar Matching Convolution](https://mlsanity.com/paper/2108.12952/) (2021)
- [Fast and Accurate Intrinsic Symmetry Detection](https://mlsanity.com/paper/1807.10162/) (2018)
- [Globally optimal point set registration by joint symmetry plane fitting](https://mlsanity.com/paper/2002.07988/) (2020)
- [Probably Approximately Symmetric: Fast rigid Symmetry Detection with Global Guarantees](https://mlsanity.com/paper/1403.6637/) (2014)
- [Learning-based Real-time Detection of Intrinsic Reflectional Symmetry](https://mlsanity.com/paper/1911.00189/) (2019)

## Built on by (most cited first, 2 of 2)

- [3D Shape Generation: A Survey](https://mlsanity.com/paper/2506.22678/) (2025)
- [Enhanced 3D Shape Analysis via Information Geometry](https://mlsanity.com/paper/2512.16213/) (2025)

## Abstract (arXiv)

Detecting the reflection symmetry plane of an object represented by a 3D point cloud is a fundamental problem in 3D computer vision and geometry processing due to its various applications, such as compression, object detection, robotic grasping, 3D surface reconstruction, etc. There exist several efficient approaches for solving this problem for clean 3D point clouds. However, it is a challenging problem to solve in the presence of outliers and missing parts. The existing methods try to overcome this challenge mostly by voting-based techniques but do not work efficiently. In this work, we proposed a statistical estimator-based approach for the plane of reflection symmetry that is robust to outliers and missing parts. We pose the problem of finding the optimal estimator for the reflection symmetry as an optimization problem on a 2-Sphere that quickly converges to the global solution for an approximate initialization. We further adapt the heat kernel signature for symmetry invariant matching of mirror symmetric points. This approach helps us to decouple the chicken-and-egg problem of finding the optimal symmetry plane and correspondences between the reflective symmetric points. The proposed approach achieves comparable mean ground-truth error and 4.5% increment in the F-score as compared to the state-of-the-art approaches on the benchmark dataset.