# A Rotation-Invariant Framework for Deep Point Cloud Analysis

arXiv: https://arxiv.org/abs/2003.07238 · HTML: https://mlsanity.com/paper/2003.07238/

## Key facts

- Cited by 62 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Mar 2020.

## Built on by (most cited first, 30 of 62)

- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Equivariance with Learned Canonicalization Functions](https://mlsanity.com/paper/2211.06489/) (2022)
- [Point Cloud Upsampling via Disentangled Refinement](https://mlsanity.com/paper/2106.04779/) (2021)
- [3D Question Answering](https://mlsanity.com/paper/2112.08359/) (2021)
- [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)
- [RIConv++: Effective Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/2202.13094/) (2022)
- [GPA-Net:No-Reference Point Cloud Quality Assessment with Multi-task Graph Convolutional Network](https://mlsanity.com/paper/2210.16478/) (2022)
- [Unified Fourier-based Kernel and Nonlinearity Design for Equivariant Networks on Homogeneous Spaces](https://mlsanity.com/paper/2206.08362/) (2022)
- [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)
- [Robustness Certification for Point Cloud Models](https://mlsanity.com/paper/2103.16652/) (2021)
- [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)
- [RAPiD-Seg: Range-Aware Pointwise Distance Distribution Networks for 3D LiDAR Segmentation](https://mlsanity.com/paper/2407.10159/) (2024)
- [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)
- [LighTN: Light-weight Transformer Network for Performance-overhead Tradeoff in Point Cloud Downsampling](https://mlsanity.com/paper/2202.06263/) (2022)
- [Learning Harmonic Molecular Representations on Riemannian Manifold](https://mlsanity.com/paper/2303.15520/) (2023)
- [PaRot: Patch-Wise Rotation-Invariant Network via Feature Disentanglement and Pose Restoration](https://mlsanity.com/paper/2302.02535/) (2023)
- [Lie Neurons: Adjoint-Equivariant Neural Networks for Semisimple Lie Algebras](https://mlsanity.com/paper/2310.04521/) (2023)
- [Deep Weighted Consensus: Dense correspondence confidence maps for 3D shape registration](https://mlsanity.com/paper/2105.02714/) (2021)
- [RPR-Net: A Point Cloud-based Rotation-aware Large Scale Place Recognition Network](https://mlsanity.com/paper/2108.12790/) (2021)
- [Rethinking Rotation Invariance with Point Cloud Registration](https://mlsanity.com/paper/2301.00149/) (2022)
- [An intuitive multi-frequency feature representation for SO(3)-equivariant networks](https://mlsanity.com/paper/2405.04537/) (2024)
- [RISurConv: Rotation Invariant Surface Attention-Augmented Convolutions for 3D Point Cloud Classification and Segmentation](https://mlsanity.com/paper/2408.06110/) (2024)
- [Rotation-Adaptive Point Cloud Domain Generalization via Intricate Orientation Learning](https://mlsanity.com/paper/2502.02247/) (2025)
- [MaskLRF: Self-supervised Pretraining via Masked Autoencoding of Local Reference Frames for Rotation-invariant 3D Point Set Analysis](https://mlsanity.com/paper/2403.00206/) (2024)
- [ShapeEmbed: a self-supervised learning framework for 2D contour quantification](https://mlsanity.com/paper/2507.01009/) (2025)

## Abstract (arXiv)

Recently, many deep neural networks were designed to process 3D point clouds, but a common drawback is that rotation invariance is not ensured, leading to poor generalization to arbitrary orientations. In this paper, we introduce a new low-level purely rotation-invariant representation to replace common 3D Cartesian coordinates as the network inputs. Also, we present a network architecture to embed these representations into features, encoding local relations between points and their neighbors, and the global shape structure. To alleviate inevitable global information loss caused by the rotation-invariant representations, we further introduce a region relation convolution to encode local and non-local information. We evaluate our method on multiple point cloud analysis tasks, including shape classification, part segmentation, and shape retrieval. Experimental results show that our method achieves consistent, and also the best performance, on inputs at arbitrary orientations, compared with the state-of-the-arts.