To reduce cost in storing, processing and visualizing a large-scale point
cloud, we consider a randomized resampling strategy to select a representative
subset of points while preserving application-dependent features. The proposed
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. We obtain a general
form of optimal resampling distribution by minimizing the reconstruction error.
The proposed optimal resampling distribution is guaranteed to be shift,
rotation and scale-invariant in the 3D space. We next 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 finally apply the proposed methods to three applications:
large-scale visualization, accurate registration and robust shape modeling. The
empirical performance validates the effectiveness and efficiency of the
proposed resampling methods.

本文提出了一种基于图像的、用于选择代表性点云子集的随机重取样策略，以降低存储、处理和可视化的成本，并对其在点云的不同应用下进行了评估。