# Spherical Kernel for Efficient Graph Convolution on 3D Point Clouds

arXiv: https://arxiv.org/abs/1909.09287 · HTML: https://mlsanity.com/paper/1909.09287/

## Key facts

- Cited by 57 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Sep 2019.

## Built on by (most cited first, 30 of 57)

- [SQN: Weakly-Supervised Semantic Segmentation of Large-Scale 3D Point Clouds](https://mlsanity.com/paper/2104.04891/) (2021)
- [Adaptive Graph Convolution for Point Cloud Analysis](https://mlsanity.com/paper/2108.08035/) (2021)
- [A Survey on Graph Neural Networks and Graph Transformers in Computer Vision: A Task-Oriented Perspective](https://mlsanity.com/paper/2209.13232/) (2022)
- [Rethinking Spatial Invariance of Convolutional Networks for Object Counting](https://mlsanity.com/paper/2206.05253/) (2022)
- [Learning Semantic Segmentation of Large-Scale Point Clouds with Random Sampling](https://mlsanity.com/paper/2107.02389/) (2021)
- [SensatUrban: Learning Semantics from Urban-Scale Photogrammetric Point Clouds](https://mlsanity.com/paper/2201.04494/) (2022)
- [Imperceptible Transfer Attack and Defense on 3D Point Cloud Classification](https://mlsanity.com/paper/2111.10990/) (2021)
- [Deep Learning Based 3D Segmentation: A Survey](https://mlsanity.com/paper/2103.05423/) (2021)
- [Hierarchical Prototype Networks for Continual Graph Representation Learning](https://mlsanity.com/paper/2111.15422/) (2021)
- [Dual Transformer for Point Cloud Analysis](https://mlsanity.com/paper/2104.13044/) (2021)
- [Isometric 3D Adversarial Examples in the Physical World](https://mlsanity.com/paper/2210.15291/) (2022)
- [Boundary-Aware Geometric Encoding for Semantic Segmentation of Point Clouds](https://mlsanity.com/paper/2101.02381/) (2021)
- [SCTN: Sparse Convolution-Transformer Network for Scene Flow Estimation](https://mlsanity.com/paper/2105.04447/) (2021)
- [Omni-supervised Point Cloud Segmentation via Gradual Receptive Field Component Reasoning](https://mlsanity.com/paper/2105.10203/) (2021)
- [Continual Learning on Graphs: Challenges, Solutions, and Opportunities](https://mlsanity.com/paper/2402.11565/) (2024)
- [Rethinking Few-shot 3D Point Cloud Semantic Segmentation](https://mlsanity.com/paper/2403.00592/) (2024)
- [PRIN/SPRIN: On Extracting Point-wise Rotation Invariant Features](https://mlsanity.com/paper/2102.12093/) (2021)
- [Point Cloud Learning with Transformer](https://mlsanity.com/paper/2104.13636/) (2021)
- [Spot-Compose: A Framework for Open-Vocabulary Object Retrieval and Drawer Manipulation in Point Clouds](https://mlsanity.com/paper/2404.12440/) (2024)
- [Weakly Supervised 3D Point Cloud Segmentation via Multi-Prototype Learning](https://mlsanity.com/paper/2205.03137/) (2022)
- [AGConv: Adaptive Graph Convolution on 3D Point Clouds](https://mlsanity.com/paper/2206.04665/) (2022)
- [Object-to-Scene: Learning to Transfer Object Knowledge to Indoor Scene Recognition](https://mlsanity.com/paper/2108.00399/) (2021)
- [Box2Seg: Learning Semantics of 3D Point Clouds with Box-Level Supervision](https://mlsanity.com/paper/2201.02963/) (2022)
- [PnP-3D: A Plug-and-Play for 3D Point Clouds](https://mlsanity.com/paper/2108.07378/) (2021)
- [Exploiting Local Geometry for Feature and Graph Construction for Better 3D Point Cloud Processing with Graph Neural Networks](https://mlsanity.com/paper/2103.15226/) (2021)
- [PointMatch: A Consistency Training Framework for Weakly Supervised Semantic Segmentation of 3D Point Clouds](https://mlsanity.com/paper/2202.10705/) (2022)
- [Unsupervised deep learning for semantic segmentation of multispectral LiDAR forest point clouds](https://mlsanity.com/paper/2502.06227/) (2025)
- [AllSpark: A Multimodal Spatio-Temporal General Intelligence Model with Ten Modalities via Language as a Reference Framework](https://mlsanity.com/paper/2401.00546/) (2023)
- [Full Point Encoding for Local Feature Aggregation in 3D Point Clouds](https://mlsanity.com/paper/2303.04458/) (2023)
- [Picasso: A CUDA-based Library for Deep Learning over 3D Meshes](https://mlsanity.com/paper/2103.15076/) (2021)

## Abstract (arXiv)

We propose a spherical kernel for efficient graph convolution of 3D point clouds. Our metric-based kernels systematically quantize the local 3D space to identify distinctive geometric relationships in the data. Similar to the regular grid CNN kernels, the spherical kernel maintains translation-invariance and asymmetry properties, where the former guarantees weight sharing among similar local structures in the data and the latter facilitates fine geometric learning. The proposed kernel is applied to graph neural networks without edge-dependent filter generation, making it computationally attractive for large point clouds. In our graph networks, each vertex is associated with a single point location and edges connect the neighborhood points within a defined range. The graph gets coarsened in the network with farthest point sampling. Analogous to the standard CNNs, we define pooling and unpooling operations for our network. We demonstrate the effectiveness of the proposed spherical kernel with graph neural networks for point cloud classification and semantic segmentation using ModelNet, ShapeNet, RueMonge2014, ScanNet and S3DIS datasets. The source code and the trained models can be downloaded from https://github.com/hlei-ziyan/SPH3D-GCN.