  Three-dimensional (3D) point clouds are important data representations in
visualization applications. The rapidly growing utility and popularity of point
cloud processing strongly motivate a plethora of research activities on
large-scale point cloud processing and feature extraction. In this work, we
investigate point cloud resampling based on hypergraph signal processing
(HGSP). We develop a novel method to extract sharp object features and reduce
the data size of point cloud representation. By directly estimating hypergraph
spectrum based on hypergraph stationary processing, we design a spectral
kernel-based filter to capture high-dimensional interactions among point signal
nodes and to better preserve object surface outlines. Experimental results
validate the effectiveness of hypergraph in representing point clouds, and
demonstrate the robustness of the proposed algorithm under noise.
