  Hypergraph spectral analysis has emerged as an effective tool processing
complex data structures in data analysis. The surface of a three-dimensional
(3D) point cloud and the multilateral relationship among their points can be
naturally captured by the high-dimensional hyperedges. This work investigates
the power of hypergraph spectral analysis in unsupervised segmentation of 3D
point clouds. We estimate and order the hypergraph spectrum from observed point
cloud coordinates. By trimming the redundancy from the estimated hypergraph
spectral space based on spectral component strengths, we develop a
clustering-based segmentation method. We apply the proposed method to various
point clouds, and analyze their respective spectral properties. Our
experimental results demonstrate the effectiveness and efficiency of the
proposed segmentation method.
