Zhang Songyang, Cui Shuguang, Ding Zhi
IEEE Trans Image Process. 2021;30:1193-1206. doi: 10.1109/TIP.2020.3042088. Epub 2020 Dec 17.
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 applications of sampling and denoising of point clouds for which we provide specific hypergraph filter design and spectral properties. Experimental results demonstrate the strength of hypergraph signal processing as a tool in characterizing the underlying properties of 3D point clouds.
随着虚拟现实应用越来越普及，三维（3D）点云已成为表征3D物体及其周围环境的一种基本数据结构。为了高效处理3D点云，一个适用于底层结构和离群噪声的模型始终至关重要。在这项工作中，我们提出了一种基于超图的新点云模型，该模型便于进行高效分析和处理。我们引入基于张量的方法来估计理想和噪声环境下点云的超图谱分量和频率系数。我们建立了超图频率与结构特征之间的解析联系。我们进一步评估了超图谱估计在点云采样和去噪这两个常见应用中的功效，为此我们提供了特定的超图滤波器设计和频谱特性。实验结果证明了超图信号处理作为一种表征3D点云底层特性的工具的优势。
