# Fast Resampling of 3D Point Clouds via Graphs

arXiv: https://arxiv.org/abs/1702.06397 · HTML: https://mlsanity.com/paper/1702.06397/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2017.

## Built on by (most cited first, 25 of 25)

- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [PC2WF: 3D Wireframe Reconstruction from Raw Point Clouds](https://mlsanity.com/paper/2103.02766/) (2021)
- [Spectrally Pruned Gaussian Fields with Neural Compensation](https://mlsanity.com/paper/2405.00676/) (2024)
- [MPED: Quantifying Point Cloud Distortion based on Multiscale Potential Energy Discrepancy](https://mlsanity.com/paper/2103.02850/) (2021)
- [Sketch and Patch: Efficient 3D Gaussian Representation for Man-Made Scenes](https://mlsanity.com/paper/2501.13045/) (2025)
- [Exploring the Devil in Graph Spectral Domain for 3D Point Cloud Attacks](https://mlsanity.com/paper/2202.07261/) (2022)
- [PUFA-GAN: A Frequency-Aware Generative Adversarial Network for 3D Point Cloud Upsampling](https://mlsanity.com/paper/2203.00914/) (2022)
- [Point Cloud Attacks in Graph Spectral Domain: When 3D Geometry Meets Graph Signal Processing](https://mlsanity.com/paper/2207.13326/) (2022)
- [FastMAC: Stochastic Spectral Sampling of Correspondence Graph](https://mlsanity.com/paper/2403.08770/) (2024)
- [EdgeGaussians -- 3D Edge Mapping via Gaussian Splatting](https://mlsanity.com/paper/2409.12886/) (2024)
- [Blind Quality Assessment of 3D Dense Point Clouds with Structure Guided Resampling](https://mlsanity.com/paper/2208.14603/) (2022)
- [No-Reference Point Cloud Quality Assessment via Graph Convolutional Network](https://mlsanity.com/paper/2411.07728/) (2024)
- [Progressive Knowledge Transfer Based on Human Visual Perception Mechanism for Perceptual Quality Assessment of Point Clouds](https://mlsanity.com/paper/2211.16646/) (2022)
- [GraphReg: Dynamical Point Cloud Registration with Geometry-aware Graph Signal Processing](https://mlsanity.com/paper/2302.01109/) (2023)
- [An Efficient Hypergraph Approach to Robust Point Cloud Resampling](https://mlsanity.com/paper/2103.06999/) (2021)
- [Hyperspectral Image Segmentation based on Graph Processing over Multilayer Networks](https://mlsanity.com/paper/2111.15018/) (2021)
- [LineGS : 3D Line Segment Representation on 3D Gaussian Splatting](https://mlsanity.com/paper/2412.00477/) (2024)
- [Deep Point Cloud Simplification for High-quality Surface Reconstruction](https://mlsanity.com/paper/2203.09088/) (2022)
- [HPGNN: Using Hierarchical Graph Neural Networks for Outdoor Point Cloud Processing](https://mlsanity.com/paper/2206.02153/) (2022)
- [Weighted Poisson-disk Resampling on Large-Scale Point Clouds](https://mlsanity.com/paper/2412.09177/) (2024)
- [3D Test-time Adaptation via Graph Spectral Driven Point Shift](https://mlsanity.com/paper/2507.18225/) (2025)
- [Sketch&Patch++: Efficient Structure-Aware 3D Gaussian Representation](https://mlsanity.com/paper/2601.05394/) (2026)
- [STS-Mixer: Spatio-Temporal-Spectral Mixer for 4D Point Cloud Video Understanding](https://mlsanity.com/paper/2604.11637/) (2026)
- [CoFi: Coarse-to-Fine ICP for LiDAR Localization in an Efficient Long-lasting Point Cloud Map](https://mlsanity.com/paper/2110.10194/) (2021)
- [LapisGS: Layered Progressive 3D Gaussian Splatting for Adaptive Streaming](https://mlsanity.com/paper/2408.14823/) (2024)

## Abstract (arXiv)

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.