[Paper Review] RGCNN: Regularized Graph CNN for Point Cloud Segmentation

Gusi Te, Wei Hu+2 more|arXiv (Cornell University)|Jun 8, 2018

3D Shape Modeling and AnalysisEngineering23 references90 citations

TL;DR

RGCNN directly processes irregular 3D point clouds using a dynamically updated graph Laplacian and a graph-signal smoothness prior to perform segmentation and classification with competitive accuracy and improved robustness.

ABSTRACT

Point cloud, an efficient 3D object representation, has become popular with the development of depth sensing and 3D laser scanning techniques. It has attracted attention in various applications such as 3D tele-presence, navigation for unmanned vehicles and heritage reconstruction. The understanding of point clouds, such as point cloud segmentation, is crucial in exploiting the informative value of point clouds for such applications. Due to the irregularity of the data format, previous deep learning works often convert point clouds to regular 3D voxel grids or collections of images before feeding them into neural networks, which leads to voluminous data and quantization artifacts. In this paper, we instead propose a regularized graph convolutional neural network (RGCNN) that directly consumes point clouds. Leveraging on spectral graph theory, we treat features of points in a point cloud as signals on graph, and define the convolution over graph by Chebyshev polynomial approximation. In particular, we update the graph Laplacian matrix that describes the connectivity of features in each layer according to the corresponding learned features, which adaptively captures the structure of dynamic graphs. Further, we deploy a graph-signal smoothness prior in the loss function, thus regularizing the learning process. Experimental results on the ShapeNet part dataset show that the proposed approach significantly reduces the computational complexity while achieving competitive performance with the state of the art. Also, experiments show RGCNN is much more robust to both noise and point cloud density in comparison with other methods. We further apply RGCNN to point cloud classification and achieve competitive results on ModelNet40 dataset.

Motivation & Objective

• Motivate direct learning on irregular 3D point clouds without voxelization or rendering.
• Propose a regularized graph CNN that updates graph structure across layers to capture dynamic topology.
• Introduce a graph-signal smoothness prior in the loss to enforce Laplacian smoothing.
• Demonstrate competitive segmentation performance with reduced computational complexity and improved robustness to noise/density.
• Extend the architecture to point cloud classification on ModelNet40.

Proposed method

• Represent point clouds as graphs using coordinates and normals as node features.
• Construct fully-connected graphs with edge weights a_{i,j}=exp(-β||p_i-p_j||^2) to capture global relationships.
• Use spectral graph convolutions with Chebyshev polynomial approximation for localized filtering.
• Update the graph Laplacian in each layer to adapt to evolving feature-induced topology.
• Incorporate a graph-signal smoothness prior y^T L y into the loss to promote Laplacian smoothing across layers.
• Provide permutation-invariance proof ensuring outputs align with input point order.

Experimental results

Research questions

• RQ1 Can a graph-CNN operate directly on irregular point clouds without voxelization?
• RQ2 Does updating the graph Laplacian per layer improve segmentation performance and robustness?
• RQ3 Does a graph-signal smoothness prior improve segmentation by enforcing topological consistency?
• RQ4 How does RGCNN compare to state-of-the-art methods on ShapeNet Part for segmentation and on ModelNet40 for classification?

Key findings

• RGCNN achieves competitive mean IoU on ShapeNet Part compared to PointNet, PointNet++, and SynSpecCNN.
• Fully-connected graph construction yields better performance than k-NN graphs (80.4% mean IoU vs lower with k-NN).
• RGCNN demonstrated robustness to noise and reduced point density, outperforming baselines under perturbations and missing data.
• On ModelNet40, the method achieves competitive classification accuracy relative to PointNet and PointNet++, though slightly lower than the best contemporary methods.
• The architecture exhibits favorable space-time complexity, with fast forward times and scalable model size.