# Rotation Invariant Point Cloud Classification: Where Local Geometry Meets Global Topology

arXiv: https://arxiv.org/abs/1911.00195 · HTML: https://mlsanity.com/paper/1911.00195/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Nov 2019.

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

- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Equivariant Point Cloud Analysis via Learning Orientations for Message Passing](https://mlsanity.com/paper/2203.14486/) (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)
- [ART-Point: Improving Rotation Robustness of Point Cloud Classifiers via Adversarial Rotation](https://mlsanity.com/paper/2203.03888/) (2022)
- [SVNet: Where SO(3) Equivariance Meets Binarization on Point Cloud Representation](https://mlsanity.com/paper/2209.05924/) (2022)
- [EPiC: Ensemble of Partial Point Clouds for Robust Classification](https://mlsanity.com/paper/2303.11419/) (2023)
- [Rotation-Adaptive Point Cloud Domain Generalization via Intricate Orientation Learning](https://mlsanity.com/paper/2502.02247/) (2025)
- [TetraSphere: A Neural Descriptor for O(3)-Invariant Point Cloud Analysis](https://mlsanity.com/paper/2211.14456/) (2022)
- [PointTree: Transformation-Robust Point Cloud Encoder with Relaxed K-D Trees](https://mlsanity.com/paper/2208.05962/) (2022)
- [Evaluating 3D Shape Analysis Methods for Robustness to Rotation Invariance](https://mlsanity.com/paper/2305.18557/) (2023)

## Abstract (arXiv)

Point cloud analysis is a fundamental task in 3D computer vision. Most previous works have conducted experiments on synthetic datasets with well-aligned data; while real-world point clouds are often not pre-aligned. How to achieve rotation invariance remains an open problem in point cloud analysis. To meet this challenge, we propose a novel approach toward achieving rotation-invariant (RI) representations by combining local geometry with global topology. In our local-global-representation (LGR)-Net, we have designed a two-branch network where one stream encodes local geometric RI features and the other encodes global topology-preserving RI features. Motivated by the observation that local geometry and global topology have different yet complementary RI responses in varying regions, two-branch RI features are fused by an innovative multi-layer perceptron (MLP) based attention module. To the best of our knowledge, this work is the first principled approach toward adaptively combining global and local information under the context of RI point cloud analysis. Extensive experiments have demonstrated that our LGR-Net achieves the state-of-the-art performance on various rotation-augmented versions of ModelNet40, ShapeNet, ScanObjectNN, and S3DIS.