# Partial Symmetry Detection for 3D Geometry using Contrastive Learning with Geodesic Point Cloud Patches

arXiv: https://arxiv.org/abs/2312.08230 · HTML: https://mlsanity.com/paper/2312.08230/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 45 references that are in the map.
- First posted on arXiv 13 Dec 2023.

## Builds on (most cited first, 14 of 14)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [PartNet: A Large-scale Benchmark for Fine-grained and Hierarchical Part-level 3D Object Understanding](https://mlsanity.com/paper/1812.02713/) (2018)
- [PointContrast: Unsupervised Pre-training for 3D Point Cloud Understanding](https://mlsanity.com/paper/2007.10985/) (2020)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [CrossPoint: Self-Supervised Cross-Modal Contrastive Learning for 3D Point Cloud Understanding](https://mlsanity.com/paper/2203.00680/) (2022)
- [PPF-FoldNet: Unsupervised Learning of Rotation Invariant 3D Local Descriptors](https://mlsanity.com/paper/1808.10322/) (2018)
- [SDM-NET: Deep Generative Network for Structured Deformable Mesh](https://mlsanity.com/paper/1908.04520/) (2019)
- [PartNet: A Recursive Part Decomposition Network for Fine-grained and Hierarchical Shape Segmentation](https://mlsanity.com/paper/1903.00709/) (2019)
- [Deep Metric Learning Beyond Binary Supervision](https://mlsanity.com/paper/1904.09626/) (2019)
- [DSG-Net: Learning Disentangled Structure and Geometry for 3D Shape Generation](https://mlsanity.com/paper/2008.05440/) (2020)
- [PRS-Net: Planar Reflective Symmetry Detection Net for 3D Models](https://mlsanity.com/paper/1910.06511/) (2019)
- [Fast and Accurate Intrinsic Symmetry Detection](https://mlsanity.com/paper/1807.10162/) (2018)

## Built on by (most cited first, 1 of 1)

- [SymGS : Leveraging Local Symmetries for 3D Gaussian Splatting Compression](https://mlsanity.com/paper/2511.13264/) (2025)

## Abstract (arXiv)

Detecting partial extrinsic symmetry in 3D geometry is a fundamental yet persistent challenge in computer vision and graphics, critical for tasks ranging from shape completion to procedural generation. Classical transformation-space voting methods rely on pairwise matching, scaling as O(n^2) and struggling to resolve coherent multi-instance groups. Recent learning approaches advance global symmetry detection but restrict the solution space to reflection planes, failing to capture rotational or translational repetitions such as the legs of a chair or the steps of a staircase. We propose SymCL, a self-supervised contrastive learning framework that detects partial symmetries across rotation, translation, and reflection (with scale-invariant features) and requires no ground truth annotations. By mapping local geodesic patches to a latent space invariant to the Euclidean group, we reformulate symmetry detection as a density-based clustering problem, enabling the simultaneous discovery of multi-instance symmetric relationships in a single forward pass. We evaluate quantitatively on SymPartNet, a new benchmark annotating all PartNet categories with partial symmetry relations, and demonstrate class-agnostic generalization qualitatively on everyday objects outside the training distribution.