# Fast Resampling of 3D Point Clouds via Graphs

## TL;DR

This paper introduces a graph-based randomized resampling method for 3D point clouds that efficiently preserves application-specific features while reducing data size, ensuring invariance to transformations.

## Contribution

It proposes a novel optimal resampling distribution based on graph filters that is invariant to shift, rotation, and scale, applicable to various 3D processing tasks.

## Key findings

- Resampling preserves features effectively across applications.
- Method outperforms existing techniques in efficiency and accuracy.
- Validated on visualization, registration, and shape modeling tasks.

## Abstract

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.