# Rotation Invariant Convolutions for 3D Point Clouds Deep Learning

arXiv: https://arxiv.org/abs/1908.06297 · HTML: https://mlsanity.com/paper/1908.06297/

## Key facts

- Cited by 80 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2019.

## Built on by (most cited first, 30 of 80)

- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [Scalars are universal: Equivariant machine learning, structured like classical physics](https://mlsanity.com/paper/2106.06610/) (2021)
- [Equivariance with Learned Canonicalization Functions](https://mlsanity.com/paper/2211.06489/) (2022)
- [Benchmarking and Analyzing Point Cloud Classification under Corruptions](https://mlsanity.com/paper/2202.03377/) (2022)
- [Equivariant Point Cloud Analysis via Learning Orientations for Message Passing](https://mlsanity.com/paper/2203.14486/) (2022)
- [Frame Mining: a Free Lunch for Learning Robotic Manipulation from 3D Point Clouds](https://mlsanity.com/paper/2210.07442/) (2022)
- [ConDor: Self-Supervised Canonicalization of 3D Pose for Partial Shapes](https://mlsanity.com/paper/2201.07788/) (2022)
- [PointConvFormer: Revenge of the Point-based Convolution](https://mlsanity.com/paper/2208.02879/) (2022)
- [RIConv++: Effective Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/2202.13094/) (2022)
- [VN-Transformer: Rotation-Equivariant Attention for Vector Neurons](https://mlsanity.com/paper/2206.04176/) (2022)
- [R-PointHop: A Green, Accurate, and Unsupervised Point Cloud Registration Method](https://mlsanity.com/paper/2103.08129/) (2021)
- [RIGA: Rotation-Invariant and Globally-Aware Descriptors for Point Cloud Registration](https://mlsanity.com/paper/2209.13252/) (2022)
- [Unified Fourier-based Kernel and Nonlinearity Design for Equivariant Networks on Homogeneous Spaces](https://mlsanity.com/paper/2206.08362/) (2022)
- [On the effectiveness of persistent homology](https://mlsanity.com/paper/2206.10551/) (2022)
- [Frame Averaging for Equivariant Shape Space Learning](https://mlsanity.com/paper/2112.01741/) (2021)
- [VectorAdam for Rotation Equivariant Geometry Optimization](https://mlsanity.com/paper/2205.13599/) (2022)
- [The Devil is in the Pose: Ambiguity-free 3D Rotation-invariant Learning via Pose-aware Convolution](https://mlsanity.com/paper/2205.15210/) (2022)
- [Unlearnable 3D Point Clouds: Class-wise Transformation Is All You Need](https://mlsanity.com/paper/2410.03644/) (2024)
- [PRIN/SPRIN: On Extracting Point-wise Rotation Invariant Features](https://mlsanity.com/paper/2102.12093/) (2021)
- [Beyond Canonicalization: How Tensorial Messages Improve Equivariant Message Passing](https://mlsanity.com/paper/2405.15389/) (2024)
- [Learning Rotation-Invariant Representations of Point Clouds Using Aligned Edge Convolutional Neural Networks](https://mlsanity.com/paper/2101.00483/) (2021)
- [ART-Point: Improving Rotation Robustness of Point Cloud Classifiers via Adversarial Rotation](https://mlsanity.com/paper/2203.03888/) (2022)
- [A Simple and Universal Rotation Equivariant Point-cloud Network](https://mlsanity.com/paper/2203.01216/) (2022)
- [SVNet: Where SO(3) Equivariance Meets Binarization on Point Cloud Representation](https://mlsanity.com/paper/2209.05924/) (2022)
- [A Closer Look at Few-Shot 3D Point Cloud Classification](https://mlsanity.com/paper/2303.18210/) (2023)
- [Robust Partial-to-Partial Point Cloud Registration in a Full Range](https://mlsanity.com/paper/2111.15606/) (2021)
- [PaRot: Patch-Wise Rotation-Invariant Network via Feature Disentanglement and Pose Restoration](https://mlsanity.com/paper/2302.02535/) (2023)
- [Local-consistent Transformation Learning for Rotation-invariant Point Cloud Analysis](https://mlsanity.com/paper/2403.11113/) (2024)
- [Deep Weighted Consensus: Dense correspondence confidence maps for 3D shape registration](https://mlsanity.com/paper/2105.02714/) (2021)

## Abstract (arXiv)

Recent progresses in 3D deep learning has shown that it is possible to design special convolution operators to consume point cloud data. However, a typical drawback is that rotation invariance is often not guaranteed, resulting in networks being trained with data augmented with rotations. In this paper, we introduce a novel convolution operator for point clouds that achieves rotation invariance. Our core idea is to use low-level rotation invariant geometric features such as distances and angles to design a convolution operator for point cloud learning. The well-known point ordering problem is also addressed by a binning approach seamlessly built into the convolution. This convolution operator then serves as the basic building block of a neural network that is robust to point clouds under 6DoF transformations such as translation and rotation. Our experiment shows that our method performs with high accuracy in common scene understanding tasks such as object classification and segmentation. Compared to previous works, most importantly, our method is able to generalize and achieve consistent results across different scenarios in which training and testing can contain arbitrary rotations.