# Modeling Local Geometric Structure of 3D Point Clouds using Geo-CNN

arXiv: https://arxiv.org/abs/1811.07782 · HTML: https://mlsanity.com/paper/1811.07782/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2018.

## Built on by (most cited first, 30 of 33)

- [M3DeTR: Multi-representation, Multi-scale, Mutual-relation 3D Object Detection with Transformers](https://mlsanity.com/paper/2104.11896/) (2021)
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- [Learning Semantic Segmentation of Large-Scale Point Clouds with Random Sampling](https://mlsanity.com/paper/2107.02389/) (2021)
- [PVT: Point-Voxel Transformer for Point Cloud Learning](https://mlsanity.com/paper/2108.06076/) (2021)
- [GNN-Surrogate: A Hierarchical and Adaptive Graph Neural Network for Parameter Space Exploration of Unstructured-Mesh Ocean Simulations](https://mlsanity.com/paper/2202.08956/) (2022)
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- [Enable Deep Learning on Mobile Devices: Methods, Systems, and Applications](https://mlsanity.com/paper/2204.11786/) (2022)
- [Clustering based Point Cloud Representation Learning for 3D Analysis](https://mlsanity.com/paper/2307.14605/) (2023)
- [PVNAS: 3D Neural Architecture Search with Point-Voxel Convolution](https://mlsanity.com/paper/2204.11797/) (2022)
- [A Survey on Approximate Edge AI for Energy Efficient Autonomous Driving Services](https://mlsanity.com/paper/2304.14271/) (2023)
- [SageMix: Saliency-Guided Mixup for Point Clouds](https://mlsanity.com/paper/2210.06944/) (2022)
- [InOR-Net: Incremental 3D Object Recognition Network for Point Cloud Representation](https://mlsanity.com/paper/2302.09886/) (2023)
- [DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Clouds](https://mlsanity.com/paper/2111.08799/) (2021)
- [CurveCloudNet: Processing Point Clouds with 1D Structure](https://mlsanity.com/paper/2303.12050/) (2023)
- [Mitigating Ambiguities in 3D Classification with Gaussian Splatting](https://mlsanity.com/paper/2503.08352/) (2025)
- [Differentiable Convolution Search for Point Cloud Processing](https://mlsanity.com/paper/2108.12856/) (2021)
- [GAM : Gradient Attention Module of Optimization for Point Clouds Analysis](https://mlsanity.com/paper/2303.10543/) (2023)
- [TCFNet: Bidirectional face-bone transformation via a Transformer-based coarse-to-fine point movement network](https://mlsanity.com/paper/2508.14373/) (2025)
- [Local Latent Representation based on Geometric Convolution for Particle Data Feature Exploration](https://mlsanity.com/paper/2105.13240/) (2021)
- [Multi Point-Voxel Convolution (MPVConv) for Deep Learning on Point Clouds](https://mlsanity.com/paper/2107.13152/) (2021)
- [Contrastive Embedding Distribution Refinement and Entropy-Aware Attention for 3D Point Cloud Classification](https://mlsanity.com/paper/2201.11388/) (2022)
- [Point Cloud Recognition with Position-to-Structure Attention Transformers](https://mlsanity.com/paper/2210.02030/) (2022)
- [Local Neighborhood Features for 3D Classification](https://mlsanity.com/paper/2212.05140/) (2022)
- [Dynamic Local Feature Aggregation for Learning on Point Clouds](https://mlsanity.com/paper/2301.02836/) (2023)
- [DAM: Diffusion Activation Maximization for 3D Global Explanations](https://mlsanity.com/paper/2401.14938/) (2024)
- [Multi Voxel-Point Neurons Convolution (MVPConv) for Fast and Accurate 3D Deep Learning](https://mlsanity.com/paper/2104.14834/) (2021)
- [VA-GCN: A Vector Attention Graph Convolution Network for learning on Point Clouds](https://mlsanity.com/paper/2106.00227/) (2021)

## Abstract (arXiv)

Recent advances in deep convolutional neural networks (CNNs) have motivated researchers to adapt CNNs to directly model points in 3D point clouds. Modeling local structure has been proven to be important for the success of convolutional architectures, and researchers exploited the modeling of local point sets in the feature extraction hierarchy. However, limited attention has been paid to explicitly model the geometric structure amongst points in a local region. To address this problem, we propose Geo-CNN, which applies a generic convolution-like operation dubbed as GeoConv to each point and its local neighborhood. Local geometric relationships among points are captured when extracting edge features between the center and its neighboring points. We first decompose the edge feature extraction process onto three orthogonal bases, and then aggregate the extracted features based on the angles between the edge vector and the bases. This encourages the network to preserve the geometric structure in Euclidean space throughout the feature extraction hierarchy. GeoConv is a generic and efficient operation that can be easily integrated into 3D point cloud analysis pipelines for multiple applications. We evaluate Geo-CNN on ModelNet40 and KITTI and achieve state-of-the-art performance.