Fast Resampling of Three-Dimensional Point Clouds via Graphs

• Published in: IEEE transactions on signal processing Vol. 66; no. 3; pp. 666 - 681
• Main Authors: Chen, Siheng, Tian, Dong, Feng, Chen, Vetro, Anthony, Kovacevic, Jelena
• Format: Journal Article
• Language: English
• Published: IEEE 01.02.2018
• Subjects: 3D point clouds; contour detection; Data visualization; graph filtering; graph signal processing; registration; sampling; Sensors; shape modeling; Signal processing; Solid modeling; Surface reconstruction; Surface treatment; Three-dimensional displays; visualization
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2017.2771730

To reduce the cost of storing, processing, and visualizing a large-scale point cloud, we propose a randomized resampling strategy that selects a representative subset of points while preserving application-dependent features. The strategy is based on graphs, which can represent underlying surfaces and lend themselves well to efficient computation. We use a general feature-extraction operator to represent application-dependent features and propose a general reconstruction error to evaluate the quality of resampling; by minimizing the error, we obtain a general form of optimal resampling distribution. The proposed resampling distribution is guaranteed to be shift-, rotation- and scale-invariant in the three-dimensional space. We then specify the feature-extraction operator to be a graph filter and study specific resampling strategies based on all-pass, low-pass, high-pass graph filtering and graph filter banks. We validate the proposed methods on three applications: Large-scale visualization, accurate registration, and robust shape modeling demonstrating the effectiveness and efficiency of the proposed resampling methods.