# Rotation-Invariant Point Convolution With Multiple Equivariant Alignments

arXiv: https://arxiv.org/abs/2012.04048 · HTML: https://mlsanity.com/paper/2012.04048/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2020.

## Built on by (most cited first, 7 of 7)

- [RIConv++: Effective Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/2202.13094/) (2022)
- [Moving Frame Net: SE(3)-Equivariant Network for Volumes](https://mlsanity.com/paper/2211.03420/) (2022)
- [Rethinking Rotation Invariance with Point Cloud Registration](https://mlsanity.com/paper/2301.00149/) (2022)
- [RISurConv: Rotation Invariant Surface Attention-Augmented Convolutions for 3D Point Cloud Classification and Segmentation](https://mlsanity.com/paper/2408.06110/) (2024)
- [Nonlinearities in Steerable SO(2)-Equivariant CNNs](https://mlsanity.com/paper/2109.06861/) (2021)
- [Sim2Real 3D Object Classification using Spherical Kernel Point Convolution and a Deep Center Voting Scheme](https://mlsanity.com/paper/2103.06134/) (2021)
- [Rotation-Invariant Completion Network](https://mlsanity.com/paper/2308.11979/) (2023)

## Abstract (arXiv)

Recent attempts at introducing rotation invariance or equivariance in 3D deep learning approaches have shown promising results, but these methods still struggle to reach the performances of standard 3D neural networks. In this work we study the relation between equivariance and invariance in 3D point convolutions. We show that using rotation-equivariant alignments, it is possible to make any convolutional layer rotation-invariant. Furthermore, we improve this simple alignment procedure by using the alignment themselves as features in the convolution, and by combining multiple alignments together. With this core layer, we design rotation-invariant architectures which improve state-of-the-art results in both object classification and semantic segmentation and reduces the gap between rotation-invariant and standard 3D deep learning approaches.