Resampling point clouds to reduce their size without compromising their utility for the tasks that use them

S. Chen, D. Tian, C. Feng, A. Vetro and J. Kovačević, Fast Resampling of Three-Dimensional Point Clouds via Graphs, IEEE Transactions on Signal Processing, vol. 66, no. 3, pp. 666-681, 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.

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