Fast Resampling of 3D Point Clouds via Graphs

Abstract

To reduce cost in storing, processing and visualizing a large-scale point cloud, we consider a randomized resampling strategy to select a representative subset of points while preserving application-dependent features. The proposed strategy is based on graphs, which can represent underlying surfaces and lend themselves well to efficient computation. We use a general feature-extraction operator to represent application-dependent features and propose a general reconstruction error to evaluate the quality of resampling. We obtain a general form of optimal resampling distribution by minimizing the reconstruction error. The proposed optimal resampling distribution is guaranteed to be shift, rotation and scale-invariant in the 3D space. We next specify the feature-extraction operator to be a graph filter and study specific resampling strategies based on all-pass, low-pass, high-pass graph filtering and graph filter banks. We finally apply the proposed methods to three applications: large-scale visualization, accurate registration and robust shape modeling. The empirical performance validates the effectiveness and efficiency of the proposed resampling methods.

References in corpus (18)

• The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
• Discrete Signal Processing on Graphs
• Discrete Signal Processing on Graphs: Sampling Theory
• Sketching as a Tool for Numerical Linear Algebra
• Efficient Sampling Set Selection for Bandlimited Graph Signals Using Graph Spectral Proxies
• Signals on Graphs: Uncertainty Principle and Sampling
• Sampling of graph signals with successive local aggregations
• Graph-based compression of dynamic 3D point cloud sequences
• Graph Frequency Analysis of Brain Signals
• Difference of Normals as a Multi-Scale Operator in Unorganized Point Clouds
• Fast approximation of matrix coherence and statistical leverage
• Greedy Sampling of Graph Signals
• On the Graph Fourier Transform for Directed Graphs
• Reconstruction of Graph Signals through Percolation from Seeding Nodes
• Blind Identification of Graph Filters
• Compressive Spectral Clustering
• Convergence Analysis of Distributed Inference with Vector-Valued Gaussian Belief Propagation
• Local Measurement and Reconstruction for Noisy Graph Signals

Cited by in corpus (23)

• PUFA-GAN: A Frequency-Aware Generative Adversarial Network for 3D Point Cloud Upsampling
• Sampling Signals on Graphs: From Theory to Applications
• Deep Unsupervised Learning of 3D Point Clouds via Graph Topology Inference and Filtering
• Hypergraph Spectral Analysis and Processing in 3D Point Cloud
• 3D Point Cloud Processing and Learning for Autonomous Driving
• An Efficient Hypergraph Approach to Robust Point Cloud Resampling
• 3D Point Cloud Denoising using Graph Laplacian Regularization of a Low Dimensional Manifold Model
• Learning Geometry-Disentangled Representation for Complementary Understanding of 3D Object Point Cloud
• Graph Signal Processing for Geometric Data and Beyond: Theory and Applications
• Point Cloud Resampling Through Hypergraph Signal Processing
• Weighted Multi-projection: 3D Point Cloud Denoising with Estimated Tangent Planes
• 3D Point Cloud Denoising via Deep Neural Network based Local Surface Estimation
• Sampling and Recovery of Graph Signals based on Graph Neural Networks
• Point Cloud Segmentation based on Hypergraph Spectral Clustering
• PC2WF: 3D Wireframe Reconstruction from Raw Point Clouds
• HPGNN: Using Hierarchical Graph Neural Networks for Outdoor Point Cloud Processing
• Attribute Compression of 3D Point Clouds Using Laplacian Sparsity Optimized Graph Transform
• Actional-Structural Graph Convolutional Networks for Skeleton-based Action Recognition
• From Spectrum Wavelet to Vertex Propagation: Graph Convolutional Networks Based on Taylor Approximation
• CoFi: Coarse-to-Fine ICP for LiDAR Localization in an Efficient Long-lasting Point Cloud Map
• Hyperspectral Image Segmentation based on Graph Processing over Multilayer Networks
• Feature Preserving and Uniformity-controllable Point Cloud Simplification on Graph
• Large-scale 3D point cloud representations via graph inception networks with applications to autonomous driving