  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.
