# Discrete Rotation Equivariance for Point Cloud Recognition

arXiv: https://arxiv.org/abs/1904.00319 · HTML: https://mlsanity.com/paper/1904.00319/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Mar 2019.

## Built on by (most cited first, 11 of 11)

- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptors](https://mlsanity.com/paper/2109.00182/) (2021)
- [Advancements in Point Cloud Data Augmentation for Deep Learning: A Survey](https://mlsanity.com/paper/2308.12113/) (2023)
- [Homogeneous vector bundles and G-equivariant convolutional neural networks](https://mlsanity.com/paper/2105.05400/) (2021)
- [Rotationally Equivariant 3D Object Detection](https://mlsanity.com/paper/2204.13630/) (2022)
- [Steerable Transformers for Volumetric Data](https://mlsanity.com/paper/2405.15932/) (2024)
- [Improving Equivariance in State-of-the-Art Supervised Depth and Normal Predictors](https://mlsanity.com/paper/2309.16646/) (2023)
- [Multi-Type Point Cloud Autoencoder: A Complete Equivariant Embedding for Molecule Conformation and Pose](https://mlsanity.com/paper/2405.13791/) (2024)
- [Disentangling Geometric Deformation Spaces in Generative Latent Shape Models](https://mlsanity.com/paper/2103.00142/) (2021)
- [Rotation Transformation Network: Learning View-Invariant Point Cloud for Classification and Segmentation](https://mlsanity.com/paper/2107.03105/) (2021)
- [DifAttack++: Query-Efficient Black-Box Adversarial Attack via Hierarchical Disentangled Feature Space in Cross-Domain](https://mlsanity.com/paper/2406.03017/) (2024)

## Abstract (arXiv)

Despite the recent active research on processing point clouds with deep networks, few attention has been on the sensitivity of the networks to rotations. In this paper, we propose a deep learning architecture that achieves discrete SO(2)/SO(3) rotation equivariance for point cloud recognition. Specifically, the rotation of an input point cloud with elements of a rotation group is similar to shuffling the feature vectors generated by our approach. The equivariance is easily reduced to invariance by eliminating the permutation with operations such as maximum or average. Our method can be directly applied to any existing point cloud based networks, resulting in significant improvements in their performance for rotated inputs. We show state-of-the-art results in the classification tasks with various datasets under both SO(2) and SO(3) rotations. In addition, we further analyze the necessary conditions of applying our approach to PointNet based networks. Source codes at https://github.com/lijx10/rot-equ-net