Source-linked AI summary
RGCNN: Regularized Graph CNN for Point Cloud Segmentation
Gusi Te, Wei Hu, Zongming Guo, Amin Zheng
TL;DR
Point-cloud segmentation must handle irregular data without the costly voxelization or rendering used by many earlier deep-learning methods. RGCNN directly applies regularized graph convolutions with adaptive graph updates, achieving competitive segmentation and classification performance alongside improved computational efficiency and robustness.
Problem
Irregular point clouds often require conversion to voxel grids or image collections for deep learning, causing voluminous data and quantization artifacts.
Method
RGCNN treats point features as graph signals, uses Chebyshev graph convolution, updates the graph Laplacian per layer, and adds a graph-signal smoothness prior.
Results
Experiments show competitive state-of-the-art segmentation performance, reduced computational complexity, robustness to low density and noise, and competitive ModelNet40 classification results.
Takeaways & Limitations
RGCNN provides a direct graph-based approach for unordered point clouds across segmentation and classification tasks.
Takeaways & Limitations
The boundary between two segments is sometimes not sharp, limiting performance to some extent.
Abstract
from arXiv · showhide
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.
1 INTRODUCTION
RGCNN addresses the challenge of processing irregular point clouds without converting them to voxel grids or images. It uses graph convolutions, adaptive graph updates, and a smoothness prior for efficient and robust segmentation.
- Point clouds support applications including 3D tele-presence, unmanned-vehicle navigation, free-viewpoint video, and heritage preservation.
- Prior deep-learning methods typically convert irregular point clouds into voxel grids or image collections to use regular-grid operations.These conversions can produce voluminous data and quantization artifacts.
- RGCNN directly consumes point clouds by treating point features as graph signals and applying graph convolution with truncated Chebyshev approximation.Its input includes feature and adjacency matrices, while its output is a per-point segmentation label.
- RGCNN regularizes learning with a graph-signal smoothness prior and updates the graph Laplacian in each layer to capture dynamic graph structure.The prior combines data-driven learning with a model-driven geometric regularization.
- Experiments report reduced computational complexity, competitive state-of-the-art performance, and greater robustness to low density and noise.
2 RELATED WORK
Related work spans model-driven, clustering-based, and deep-learning approaches to point-cloud segmentation, alongside spectral and spatial graph convolutions. These methods differ in their handling of irregularity, local context, computational cost, and global structure.
- Point Cloud Segmentation: Model-driven segmentation uses geometric assumptions but is sensitive to noise, uneven density, and complicated structures.Examples include edge-based, region-growing, and model-fitting methods.
- Point Cloud Segmentation: Clustering-based methods can outperform model-driven approaches in complex scenes but may lack local information.
- Point Cloud Segmentation: PointNet directly consumes point clouds using a symmetric function, whereas PointNet processes points independently and PointNet++ adds hierarchical grouping.
- Graph Convolutional Neural Network: Spectral graph convolutions face eigen-decomposition costs, motivating approximations such as Chebyshev expansions and Lanczos methods.
- Graph Convolutional Neural Network: RGCNN extends spectral graph convolution to point-cloud segmentation, which the paper identifies as a first extension of this kind.
3 PROBLEM STATEMENT
The problem formulation represents an irregular point cloud with point features and graph connectivity. RGCNN maps these inputs to per-point scores over semantic labels.
- Each point is represented by a feature vector that may include coordinates, color, or surface normal.
- RGCNN uses each point’s coordinates and normal as its feature, yielding m = 6 features per point.
- The model takes an n × m feature matrix P and an n × n adjacency matrix W as input.
- For k semantic labels, RGCNN outputs an n × k score matrix S containing scores for every point-label pair.
4 THE PROPOSED RGCNN
RGCNN directly processes unordered point clouds as graph signals, constructing and adapting graphs to learn local and global features for segmentation and classification.
- Overall architecture: RGCNN takes point-cloud coordinates and normals as graph features, together with an adjacency matrix, and outputs per-point semantic scores.The input feature matrix and adjacency matrix represent the irregular point cloud; each point receives scores for the semantic labels.
- Overall architecture: The architecture uses one shared feature-extraction model followed by separate segmentation and classification branches.Segmentation aggregates graph-convolution features and concatenates representations from different layers to capture local and global information.
- Graph construction: Complete graphs connect every point, with edge weights based on feature distances to measure structural similarity.The graph-construction discussion motivates considering relationships among all points in the cloud.
- Graph convolution: Graph convolution uses truncated Chebyshev polynomials to provide localized filtering without the eigen-decomposition required by direct spectral filtering.Direct spectral filtering has O(n^3) complexity, whereas Chebyshev approximation reduces the complexity to O(K|E|).
- Feature learning: Each graph-convolution output applies a learned weight matrix, bias, and ReLU activation, while polynomial order K > 1 incorporates neighborhood information.When K = 1, the operation is equivalent to a shared one-layer perceptron and loses neighborhood information.
- Feature learning: Deeper layers capture semantically similar structures more effectively in high-dimensional feature spaces.The reported observation concerns how feature spaces vary across network layers.
5 THE PROPOSED LOSS FUNCTION AND THEORETICAL ANALYSIS
RGCNN adds a graph-signal smoothness prior across its graph-convolution layers and analyzes its spectral and permutation-invariance properties. The prior favors graph-adapted smooth features, while the architecture preserves pointwise outputs under input reordering.
- 5.1 The proposed loss function: The loss supplements cross entropy with a graph-signal smoothness prior computed from all three graph-convolution layers.The smoothness penalty is controlled by γ, empirically set to 10^-9.
- 5.1 The proposed loss function: The prior encourages adjacent vertices with larger edge weights to have more similar feature values, adapting the signal to graph topology.For small edge weights, neighboring features may remain more different.
- 5.2 Theoretical analysis: Minimizing the prior penalizes higher-frequency graph Fourier components more heavily, thereby preserving low-frequency components and smoothing the signal spectrally.The weighting follows the graph Laplacian eigenvalues, whose larger values correspond to higher-frequency coefficients.
- 5.2 Theoretical analysis: The smoothing operation makes vertex features within each connected graph component more similar, which eases the segmentation task.
- 5.2 Theoretical analysis: RGCNN is permutation-invariant: permuting input feature rows causes the output rows to permute in the same way.Thus, its segmentation result is irrelevant to the ordering of input points.
6 EXPERIMENTAL RESULTS
RGCNN is evaluated for point-cloud segmentation on ShapeNet part, including accuracy, graph construction, robustness to noise and density, classification, and complexity. It achieves competitive segmentation and classification performance while showing robustness and fast inference, with some boundary limitations.
- Experimental setup: RGCNN is evaluated on ShapeNet part using mIoU across 16 categories and 50 part labels, with coordinates and normals as input features.The experiments use 2048 randomly sampled points per model and compare against ShapeNet, PointNet, PointNet++, and SynSpecCNN.
- Segmentation results: RGCNN achieves competitive ShapeNet segmentation results and outperforms competing methods in 5 categories.Visual results are reported as more consistent than PointNet on some challenging objects.
- Graph construction: 80.4% mean mIoU with k-nearest-neighbor graphs is much lower than using the proposed fully-connected graph.The authors attribute the difference to the fully-connected graph capturing more abundant information.
- Robustness to noise: RGCNN remains robust under Gaussian coordinate noise up to σ ∈ [0.02, 0.2], while PointNet’s performance drops quickly as noise variance increases.At σ = 0.1, the segmentation is visually close to ground truth from the macroscopic view.
- Robustness to density: At a missing ratio of 0.75, RGCNN retains 85% accuracy versus PointNet’s 73%.The result is accompanied by satisfactory visual segmentation compared with ground truth.
- Classification and complexity: The classification extension achieves competitive ModelNet40 results, while the model has the fastest forward time with an acceptable model size among compared methods.Using fixed graphs reduces forward time to approximately 4.8 ms, supporting real-time classification use.
- Discussion and limitations: The discussion identifies blurred boundaries between segments as a limitation that restricts performance to some extent.The comparison also emphasizes dynamically updated graph structure and neighborhood features as design distinctions.
7 CONCLUSION
The paper concludes that RGCNN directly processes irregular point clouds with dynamic graph updates and graph-signal regularization. Experiments report competitive performance, lower computational complexity, robustness to sparse and noisy inputs, and competitive classification results.
- Conclusion: RGCNN directly consumes irregular 3D point clouds, updates the graph Laplacian per layer, and adds a graph-signal smoothness prior to the loss.The paper also proves permutation invariance for unordered point-cloud inputs.
- Conclusion: RGCNN achieves competitive state-of-the-art segmentation performance with much lower computational complexity and greater robustness to low density and noise than competing methods.The architecture also achieves competitive classification results on ModelNet40.