Fast Resampling of 3D Point Clouds via Graphs
This work addresses the challenge of efficiently handling large 3D point clouds for applications in fields like computer vision and graphics, though it appears incremental as it builds on existing graph-based techniques.
The paper tackles the problem of reducing storage and processing costs for large-scale 3D point clouds by developing a randomized resampling strategy that selects a representative subset while preserving application-dependent features, using graph-based methods to achieve shift, rotation, and scale invariance and demonstrating effectiveness in applications like visualization, registration, and shape modeling.
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.