# Curvature Informed Furthest Point Sampling

arXiv: https://arxiv.org/abs/2411.16995 · HTML: https://mlsanity.com/paper/2411.16995/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 54 references that are in the map.
- First posted on arXiv 25 Nov 2024.

## Builds on (most cited first, 30 of 36)

- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [PointPillars: Fast Encoders for Object Detection from Point Clouds](https://mlsanity.com/paper/1812.05784/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [PointCNN: Convolution On X-Transformed Points](https://mlsanity.com/paper/1801.07791/) (2018)
- [PCT: Point cloud transformer](https://mlsanity.com/paper/2012.09688/) (2020)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [PCN: Point Completion Network](https://mlsanity.com/paper/1808.00671/) (2018)
- [Point-Voxel CNN for Efficient 3D Deep Learning](https://mlsanity.com/paper/1907.03739/) (2019)
- [Regularisation of Neural Networks by Enforcing Lipschitz Continuity](https://mlsanity.com/paper/1804.04368/) (2018)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [ULIP: Learning a Unified Representation of Language, Images, and Point Clouds for 3D Understanding](https://mlsanity.com/paper/2212.05171/) (2022)
- [SpiderCNN: Deep Learning on Point Sets with Parameterized Convolutional Filters](https://mlsanity.com/paper/1803.11527/) (2018)
- [What Do Single-view 3D Reconstruction Networks Learn?](https://mlsanity.com/paper/1905.03678/) (2019)
- [PAConv: Position Adaptive Convolution with Dynamic Kernel Assembling on Point Clouds](https://mlsanity.com/paper/2103.14635/) (2021)
- [PU-Net: Point Cloud Upsampling Network](https://mlsanity.com/paper/1801.06761/) (2018)
- [Stratified Transformer for 3D Point Cloud Segmentation](https://mlsanity.com/paper/2203.14508/) (2022)
- [SPLATNet: Sparse Lattice Networks for Point Cloud Processing](https://mlsanity.com/paper/1802.08275/) (2018)
- [Cascaded Refinement Network for Point Cloud Completion](https://mlsanity.com/paper/2004.03327/) (2020)
- [Variational Relational Point Completion Network](https://mlsanity.com/paper/2104.10154/) (2021)
- [PCPNET: Learning Local Shape Properties from Raw Point Clouds](https://mlsanity.com/paper/1710.04954/) (2017)
- [SampleNet: Differentiable Point Cloud Sampling](https://mlsanity.com/paper/1912.03663/) (2019)
- [PRA-Net: Point Relation-Aware Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2112.04903/) (2021)
- [Adaptive Hierarchical Down-Sampling for Point Cloud Classification](https://mlsanity.com/paper/1904.08506/) (2019)

## Built on by (most cited first, 1 of 1)

- [TokenMatch: 3D Mesh Correspondence Transformer with Curvature-Guided Tokenisation](https://mlsanity.com/paper/2609.04202/) (2026)

## Abstract (arXiv)

Point cloud representation has gained traction due to its efficient memory usage and simplicity in acquisition, manipulation, and storage. However, as point cloud sizes increase, effective down-sampling becomes essential to address the computational requirements of downstream tasks. Classical approaches, such as furthest point sampling (FPS), perform well on benchmarks but rely on heuristics and overlook geometric features, like curvature, during down-sampling. In this paper, We introduce a reinforcement learning-based sampling algorithm that enhances FPS by integrating curvature information. Our approach ranks points by combining FPS-derived soft ranks with curvature scores computed by a deep neural network, allowing us to replace a proportion of low-curvature points in the FPS set with high-curvature points from the unselected set. Existing differentiable sampling techniques often suffer from training instability, hindering their integration into end-to-end learning frameworks. By contrast, our method achieves stable end-to-end learning, consistently outperforming baseline models across multiple downstream geometry processing tasks. We provide comprehensive ablation studies, with both qualitative and quantitative insights into the effect of each feature on performance. Our algorithm establishes state-of-the-art results for classification, segmentation and shape completion, showcasing its robustness and adaptability.