Graph Spectral Image Processing

7Graph Spectral Point Cloud Processing

Wei HU¹, Siheng CHEN² and Dong TIAN³

¹Peking University, Beijing, China

²Shanghai Jiao Tong University, China

³InterDigital Inc., New York, USA

7.1. Introduction

Images provide 2D visual projection of the 3D world and could have geometric information embedded implicitly. In contrast, 3D point clouds form omnidirectional representations of the explicit geometric structure and visual information of the 3D world. A point cloud consists of a set of 3D points that are irregularly sampled from the surface of objects or scenes, as demonstrated in Figure 7.1. Each point typically contains geometry information (i.e. its 3D coordinate) and may be additionally associated with other attribute information, such as RGB colors and/or reflection intensity, depending on the scanning device. The maturity of depth sensing and laser scanning techniques¹ makes the acquisition of 3D point clouds more affordable. A point cloud is gradually becoming a popular 3D representation format and has a critical role in a wide range of applications, including immersive tele-presence (Mekuria et al. 2016), autonomous driving (Chen et al. 2021) and digital preservation of cultural heritage (Gomes et al. 2014).

By their very nature, point clouds have a profound connection with graphs. A point cloud is typically a representation (signal) of some underlying surface or 2D manifold over a set of quantized (sampled) nodes, which reside on an unstructured grid. More specifically, ...