Hypergraph Spectral Analysis and Processing in 3D Point Cloud

Abstract

Along with increasingly popular virtual reality applications, the\nthree-dimensional (3D) point cloud has become a fundamental data structure to\ncharacterize 3D objects and surroundings. To process 3D point clouds\nefficiently, a suitable model for the underlying structure and outlier noises\nis always critical. In this work, we propose a hypergraph-based new point cloud\nmodel that is amenable to efficient analysis and processing. We introduce\ntensor-based methods to estimate hypergraph spectrum components and frequency\ncoefficients of point clouds in both ideal and noisy settings. We establish an\nanalytical connection between hypergraph frequencies and structural features.\nWe further evaluate the efficacy of hypergraph spectrum estimation in two\ncommon point cloud applications of sampling and denoising for which also we\nelaborate specific hypergraph filter design and spectral properties. The\nempirical performance demonstrates the strength of hypergraph signal processing\nas a tool in 3D point clouds and the underlying properties.\n