Spherical Kernel for Efficient Graph Convolution on 3D Point Clouds (1909.09287v2)

Abstract: 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.

• The paper introduces a spherical convolution kernel that partitions 3D space into volumetric bins to maintain translation invariance and support fine geometric learning.
• It leverages graph representations using farthest point sampling to provide a hierarchical and computationally efficient structure for 3D point cloud processing.
• Experiments on benchmarks like ModelNet and ShapeNet demonstrate high accuracy with fewer parameters, showcasing scalability and real-time potential.

Efficient Graph Convolution on 3D Point Clouds Using Spherical Kernels

The paper "Spherical Kernel for Efficient Graph Convolution on 3D Point Clouds" introduces a novel approach to processing 3D point cloud data by leveraging spherical convolutional kernels within graph neural network (GNN) architectures. The paper elucidates a method of combining spherical kernels with graph-based representations to efficiently extract features from 3D point clouds, offering an alternative to traditional voxel and grid-based methods, which are computationally expensive.

Research Contributions

The work presents several notable contributions to the area of geometric deep learning:

1. Spherical Convolutional Kernel: The authors propose a discrete spherical convolutional kernel specifically designed for 3D point clouds. This kernel partitions the space surrounding a point into volumetric bins based on spherical coordinates, effectively leveraging the spatial structure of 3D data. The partitioning helps maintain translation invariance, similar to conventional CNNs, while also upholding asymmetry to facilitate fine geometric learning.
2. Graph Representation of Point Clouds: The paper utilizes graph-based methods to represent point clouds, with each vertex corresponding to a point and edges connecting neighborhood points. The use of farthest point sampling for graph coarsening and pooling/unpooling operations provides a hierarchical structure similar to standard CNNs. This approach inherently capitalizes on the sparse nature of point clouds, making it computationally efficient.
3. Evaluation on Benchmark Datasets: The proposed method is evaluated on benchmark datasets including ModelNet, ShapeNet, RueMonge2014, ScanNet, and S3DIS. The graphs for point clouds allow convolutional blocks analogous to those in image-based CNNs, leading to effective feature learning for tasks such as classification and semantic segmentation.

Key Numerical Results

The paper reports competitive performance on various benchmark datasets. For instance, in the ModelNet40 classification task and the ShapeNet part segmentation task, the proposed method achieves high accuracy with significantly fewer parameters compared to existing methods like PointNet++ and PointCNN. The proposed GNN architecture is shown to efficiently handle point cloud sizes that exceed those typically used in prior works, demonstrating the scalability and computational advantages of the approach.

Theoretical and Practical Implications

The introduction of spherical kernels within GNNs lays a foundation for developing more efficient models for 3D data analysis. This research can influence theoretical advancements in graph-based convolutional architectures by emphasizing the role of geometric partitioning in feature extraction. Practically, the method holds potential for applications in autonomous driving, robotics, and augmented reality, where real-time processing of 3D point clouds is critical.

Future Prospects

Looking forward, this framework could catalyze further research into adaptive kernel partitioning strategies that dynamically adjust based on local geometric properties of the data. Additionally, integrating adversarial learning concepts or transfer learning methods could enhance the robustness and generalization of these models across various 3D data domains.

Overall, "Spherical Kernel for Efficient Graph Convolution on 3D Point Clouds" presents a well-founded approach to improving graph convolutional networks for 3D data, combining theoretical innovation with practical applicability, and setting a new direction for further exploration in geometric deep learning.