Hypergraph Spectral Analysis and Processing in 3D Point Cloud

Abstract

Along with increasingly popular virtual reality applications, the three-dimensional (3D) point cloud has become a fundamental data structure to characterize 3D objects and surroundings. To process 3D point clouds efficiently, a suitable model for the underlying structure and outlier noises is always critical. In this work, we propose a hypergraph-based new point cloud model that is amenable to efficient analysis and processing. We introduce tensor-based methods to estimate hypergraph spectrum components and frequency coefficients of point clouds in both ideal and noisy settings. We establish an analytical connection between hypergraph frequencies and structural features. We further evaluate the efficacy of hypergraph spectrum estimation in two common point cloud applications of sampling and denoising for which also we elaborate specific hypergraph filter design and spectral properties. The empirical performance demonstrates the strength of hypergraph signal processing as a tool in 3D point clouds and the underlying properties.

References in corpus (13)

• ShapeNet: An Information-Rich 3D Model Repository
• Connecting the Dots: Identifying Network Structure via Graph Signal Processing
• Graph Laplacian Regularization for Image Denoising: Analysis in the Continuous Domain
• Stationary Graph Processes and Spectral Estimation
• Fast Resampling of 3D Point Clouds via Graphs
• Feature Graph Learning for 3D Point Cloud Denoising
• Spectra of general hypergraphs
• Introducing Hypergraph Signal Processing: Theoretical Foundation and Practical Applications
• Large-Scale 3D Shape Reconstruction and Segmentation from ShapeNet Core55
• Graph-based denoising for time-varying point clouds
• 3D Point Cloud Denoising using Graph Laplacian Regularization of a Low Dimensional Manifold Model
• Fast 3D Point Cloud Denoising via Bipartite Graph Approximation & Total Variation
• Denoising a Point Cloud for Surface Reconstruction

Cited by in corpus (5)

• An Efficient Hypergraph Approach to Robust Point Cloud Resampling
• Hypergraph-Aided Task-Resource Matching for Maximizing Value of Task Completion in Collaborative IoT Systems
• Point Cloud Resampling Through Hypergraph Signal Processing
• HPGNN: Using Hierarchical Graph Neural Networks for Outdoor Point Cloud Processing
• Point Cloud Segmentation based on Hypergraph Spectral Clustering