# Global Context Aware Convolutions for 3D Point Cloud Understanding

arXiv: https://arxiv.org/abs/2008.02986 · HTML: https://mlsanity.com/paper/2008.02986/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Aug 2020.

## Built on by (most cited first, 26 of 26)

- [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)
- [Equivariant Point Cloud Analysis via Learning Orientations for Message Passing](https://mlsanity.com/paper/2203.14486/) (2022)
- [RIConv++: Effective Rotation Invariant Convolutions for 3D Point Clouds Deep Learning](https://mlsanity.com/paper/2202.13094/) (2022)
- [VN-Transformer: Rotation-Equivariant Attention for Vector Neurons](https://mlsanity.com/paper/2206.04176/) (2022)
- [Unified Fourier-based Kernel and Nonlinearity Design for Equivariant Networks on Homogeneous Spaces](https://mlsanity.com/paper/2206.08362/) (2022)
- [Beyond Canonicalization: How Tensorial Messages Improve Equivariant Message Passing](https://mlsanity.com/paper/2405.15389/) (2024)
- [RI-MAE: Rotation-Invariant Masked AutoEncoders for Self-Supervised Point Cloud Representation Learning](https://mlsanity.com/paper/2409.00353/) (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)
- [PaRot: Patch-Wise Rotation-Invariant Network via Feature Disentanglement and Pose Restoration](https://mlsanity.com/paper/2302.02535/) (2023)
- [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)
- [Nonlinearities in Steerable SO(2)-Equivariant CNNs](https://mlsanity.com/paper/2109.06861/) (2021)
- [FoV-Net: Rotation-Invariant CAD B-rep Learning via Field-of-View Ray Casting](https://mlsanity.com/paper/2602.24084/) (2026)
- [Efficient Continuous Group Convolutions for Local SE(3) Equivariance in 3D Point Clouds](https://mlsanity.com/paper/2502.07505/) (2025)
- [Rotation-Invariant Completion Network](https://mlsanity.com/paper/2308.11979/) (2023)
- [Point-PNG: Conditional Pseudo-Negatives Generation for Point Cloud Pre-Training](https://mlsanity.com/paper/2409.15832/) (2024)
- [HFBRI-MAE: Handcrafted Feature Based Rotation-Invariant Masked Autoencoder for 3D Point Cloud Analysis](https://mlsanity.com/paper/2504.14132/) (2025)
- [VNT-Net: Rotational Invariant Vector Neuron Transformers](https://mlsanity.com/paper/2205.09690/) (2022)
- [Sampling Foundational Transformer: A Theoretical Perspective](https://mlsanity.com/paper/2408.05822/) (2024)
- [Hierarchical Direction Perception via Atomic Dot-Product Operators for Rotation-Invariant Point Clouds Learning](https://mlsanity.com/paper/2511.08240/) (2025)
- [Rotational Equivariance in Machine Learning: A Comprehensive Tutorial](https://mlsanity.com/paper/2608.31045/) (2026)

## Abstract (arXiv)

Recent advances in deep learning for 3D point clouds have shown great promises in scene understanding tasks thanks to the introduction of convolution operators to consume 3D point clouds directly in a neural network. Point cloud data, however, could have arbitrary rotations, especially those acquired from 3D scanning. Recent works show that it is possible to design point cloud convolutions with rotation invariance property, but such methods generally do not perform as well as translation-invariant only convolution. We found that a key reason is that compared to point coordinates, rotation-invariant features consumed by point cloud convolution are not as distinctive. To address this problem, we propose a novel convolution operator that enhances feature distinction by integrating global context information from the input point cloud to the convolution. To this end, a globally weighted local reference frame is constructed in each point neighborhood in which the local point set is decomposed into bins. Anchor points are generated in each bin to represent global shape features. A convolution can then be performed to transform the points and anchor features into final rotation-invariant features. We conduct several experiments on point cloud classification, part segmentation, shape retrieval, and normals estimation to evaluate our convolution, which achieves state-of-the-art accuracy under challenging rotations.