# General Rotation Invariance Learning for Point Clouds via Weight-Feature Alignment

arXiv: https://arxiv.org/abs/2302.09907 · HTML: https://mlsanity.com/paper/2302.09907/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 58 references that are in the map.
- First posted on arXiv 20 Feb 2023.

## Builds on (most cited first, 30 of 42)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [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)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [PointRCNN: 3D Object Proposal Generation and Detection from Point Cloud](https://mlsanity.com/paper/1812.04244/) (2018)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [PCT: Point cloud transformer](https://mlsanity.com/paper/2012.09688/) (2020)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Steerable CNNs](https://mlsanity.com/paper/1612.08498/) (2016)
- [Learning SO(3) Equivariant Representations with Spherical CNNs](https://mlsanity.com/paper/1711.06721/) (2017)
- [Voxel Transformer for 3D Object Detection](https://mlsanity.com/paper/2109.02497/) (2021)
- [Submanifold Sparse Convolutional Networks](https://mlsanity.com/paper/1706.01307/) (2017)
- [SO-Net: Self-Organizing Network for Point Cloud Analysis](https://mlsanity.com/paper/1803.04249/) (2018)
- [Deep Parametric Continuous Convolutional Neural Networks](https://mlsanity.com/paper/2101.06742/) (2021)
- [Point Convolutional Neural Networks by Extension Operators](https://mlsanity.com/paper/1803.10091/) (2018)
- [PPF-FoldNet: Unsupervised Learning of Rotation Invariant 3D Local Descriptors](https://mlsanity.com/paper/1808.10322/) (2018)
- [Fast Point Transformer](https://mlsanity.com/paper/2112.04702/) (2021)
- [Voxel Set Transformer: A Set-to-Set Approach to 3D Object Detection from Point Clouds](https://mlsanity.com/paper/2203.10314/) (2022)
- [Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/1908.06297/) (2019)
- [A Rotation-Invariant Framework for Deep Point Cloud Analysis](https://mlsanity.com/paper/2003.07238/) (2020)
- [CubeNet: Equivariance to 3D Rotation and Translation](https://mlsanity.com/paper/1804.04458/) (2018)
- [Effective Rotation-invariant Point CNN with Spherical Harmonics kernels](https://mlsanity.com/paper/1906.11555/) (2019)
- [Leveraging SE(3) Equivariance for Self-Supervised Category-Level Object Pose Estimation](https://mlsanity.com/paper/2111.00190/) (2021)

## Built on by (most cited first, 2 of 2)

- [4D Panoptic Segmentation as Invariant and Equivariant Field Prediction](https://mlsanity.com/paper/2303.15651/) (2023)
- [RI-MAE: Rotation-Invariant Masked AutoEncoders for Self-Supervised Point Cloud Representation Learning](https://mlsanity.com/paper/2409.00353/) (2024)

## Abstract (arXiv)

Compared to 2D images, 3D point clouds are much more sensitive to rotations. We expect the point features describing certain patterns to keep invariant to the rotation transformation. There are many recent SOTA works dedicated to rotation-invariant learning for 3D point clouds. However, current rotation-invariant methods lack generalizability on the point clouds in the open scenes due to the reliance on the global distribution, ie the global scene and backgrounds. Considering that the output activation is a function of the pattern and its orientation, we need to eliminate the effect of the orientation.In this paper, inspired by the idea that the network weights can be considered a set of points distributed in the same 3D space as the input points, we propose Weight-Feature Alignment (WFA) to construct a local Invariant Reference Frame (IRF) via aligning the features with the principal axes of the network weights. Our WFA algorithm provides a general solution for the point clouds of all scenes. WFA ensures the model achieves the target that the response activity is a necessary and sufficient condition of the pattern matching degree. Practically, we perform experiments on the point clouds of both single objects and open large-range scenes. The results suggest that our method almost bridges the gap between rotation invariance learning and normal methods.