# Cloud-RAIN: Point Cloud Analysis with Reflectional Invariance

arXiv: https://arxiv.org/abs/2305.07814 · HTML: https://mlsanity.com/paper/2305.07814/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 66 references that are in the map.
- First posted on arXiv 13 May 2023.

## Builds on (most cited first, 30 of 44)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [VoxelNet: End-to-End Learning for Point Cloud Based 3D Object Detection](https://mlsanity.com/paper/1711.06396/) (2017)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [RandLA-Net: Efficient Semantic Segmentation of Large-Scale Point Clouds](https://mlsanity.com/paper/1911.11236/) (2019)
- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [Rethinking Network Design and Local Geometry in Point Cloud: A Simple Residual MLP Framework](https://mlsanity.com/paper/2202.07123/) (2022)
- [Relation-Shape Convolutional Neural Network for Point Cloud Analysis](https://mlsanity.com/paper/1904.07601/) (2019)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [FlowNet3D: Learning Scene Flow in 3D Point Clouds](https://mlsanity.com/paper/1806.01411/) (2018)
- [Stratified Transformer for 3D Point Cloud Segmentation](https://mlsanity.com/paper/2203.14508/) (2022)
- [SPLATNet: Sparse Lattice Networks for Point Cloud Processing](https://mlsanity.com/paper/1802.08275/) (2018)
- [Point Convolutional Neural Networks by Extension Operators](https://mlsanity.com/paper/1803.10091/) (2018)
- [ShellNet: Efficient Point Cloud Convolutional Neural Networks using Concentric Shells Statistics](https://mlsanity.com/paper/1908.06295/) (2019)
- [Fast Point Transformer](https://mlsanity.com/paper/2112.04702/) (2021)
- [Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/1908.06297/) (2019)
- [PointMixer: MLP-Mixer for Point Cloud Understanding](https://mlsanity.com/paper/2111.11187/) (2021)
- [Deep Polynomial Neural Networks](https://mlsanity.com/paper/2006.13026/) (2020)
- [A Rotation-Invariant Framework for Deep Point Cloud Analysis](https://mlsanity.com/paper/2003.07238/) (2020)
- [Effective Rotation-invariant Point CNN with Spherical Harmonics kernels](https://mlsanity.com/paper/1906.11555/) (2019)
- [Contrastive Boundary Learning for Point Cloud Segmentation](https://mlsanity.com/paper/2203.05272/) (2022)

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

- [Seeing through Unclear Glass: Occlusion Removal with One Shot](https://mlsanity.com/paper/2509.01033/) (2025)

## Abstract (arXiv)

The networks for point cloud tasks are expected to be invariant when the point clouds are affinely transformed such as rotation and reflection. So far, relative to the rotational invariance that has been attracting major research attention in the past years, the reflection invariance is little addressed. Notwithstanding, reflection symmetry can find itself in very common and important scenarios, e.g., static reflection symmetry of structured streets, dynamic reflection symmetry from bidirectional motion of moving objects (such as pedestrians), and left- and right-hand traffic practices in different countries. To the best of our knowledge, unfortunately, no reflection-invariant network has been reported in point cloud analysis till now. To fill this gap, we propose a framework by using quadratic neurons and PCA canonical representation, referred to as Cloud-RAIN, to endow point underlineCloud models with underlineReflectionunderlineAl underlineINvariance. We prove a theorem to explain why Cloud-RAIN can enjoy reflection symmetry. Furthermore, extensive experiments also corroborate the reflection property of the proposed Cloud-RAIN and show that Cloud-RAIN is superior to data augmentation. Our code is available at https://github.com/YimingCuiCuiCui/Cloud-RAIN.