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.