# A Linear Time and Space Local Point Cloud Geometry Encoder via Vectorized Kernel Mixture (VecKM)

arXiv: https://arxiv.org/abs/2404.01568 · HTML: https://mlsanity.com/paper/2404.01568/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 45 references that are in the map.
- First posted on arXiv 2 Apr 2024.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (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)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (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)
- [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)
- [Point-BERT: Pre-training 3D Point Cloud Transformers with Masked Point Modeling](https://mlsanity.com/paper/2111.14819/) (2021)
- [Joint 2D-3D-Semantic Data for Indoor Scene Understanding](https://mlsanity.com/paper/1702.01105/) (2017)
- [Rethinking Network Design and Local Geometry in Point Cloud: A Simple Residual MLP Framework](https://mlsanity.com/paper/2202.07123/) (2022)
- [Random Feature Attention](https://mlsanity.com/paper/2103.02143/) (2021)
- [SpiderCNN: Deep Learning on Point Sets with Parameterized Convolutional Filters](https://mlsanity.com/paper/1803.11527/) (2018)
- [PointASNL: Robust Point Clouds Processing using Nonlocal Neural Networks with Adaptive Sampling](https://mlsanity.com/paper/2003.00492/) (2020)
- [Deep Complex Networks](https://mlsanity.com/paper/1705.09792/) (2017)
- [3D Object Detection with Pointformer](https://mlsanity.com/paper/2012.11409/) (2020)
- [Walk in the Cloud: Learning Curves for Point Clouds Shape Analysis](https://mlsanity.com/paper/2105.01288/) (2021)
- [Stratified Transformer for 3D Point Cloud Segmentation](https://mlsanity.com/paper/2203.14508/) (2022)
- [PCPNET: Learning Local Shape Properties from Raw Point Clouds](https://mlsanity.com/paper/1710.04954/) (2017)
- [Surface Representation for Point Clouds](https://mlsanity.com/paper/2205.05740/) (2022)
- [3D Point Cloud Processing and Learning for Autonomous Driving](https://mlsanity.com/paper/2003.00601/) (2020)
- [Computing on Functions Using Randomized Vector Representations](https://mlsanity.com/paper/2109.03429/) (2021)
- [Topology-Aware Non-Rigid Point Cloud Registration](https://mlsanity.com/paper/1811.07014/) (2018)
- [SceneCalib: Automatic Targetless Calibration of Cameras and Lidars in Autonomous Driving](https://mlsanity.com/paper/2304.05530/) (2023)
- [Decodable and Sample Invariant Continuous Object Encoder](https://mlsanity.com/paper/2311.00187/) (2023)

## Built on by (most cited first, 6 of 6)

- [Event3DGS: Event-Based 3D Gaussian Splatting for High-Speed Robot Egomotion](https://mlsanity.com/paper/2406.02972/) (2024)
- [EV-Flying: an Event-based Dataset for In-The-Wild Recognition of Flying Objects](https://mlsanity.com/paper/2506.04048/) (2025)
- [Learning Normal Flow Directly From Event Neighborhoods](https://mlsanity.com/paper/2412.11284/) (2024)
- [A Real-Time Event-Based Normal Flow Estimator](https://mlsanity.com/paper/2504.19417/) (2025)
- [3D Gaussian Point Encoders](https://mlsanity.com/paper/2511.04797/) (2025)
- [Real-time Motion Segmentation with Event-based Normal Flow](https://mlsanity.com/paper/2602.20790/) (2026)

## Abstract (arXiv)

We propose VecKM, a local point cloud geometry encoder that is descriptive and efficient to compute. VecKM leverages a unique approach by vectorizing a kernel mixture to represent the local point cloud. Such representation's descriptiveness is supported by two theorems that validate its ability to reconstruct and preserve the similarity of the local shape. Unlike existing encoders downsampling the local point cloud, VecKM constructs the local geometry encoding using all neighboring points, producing a more descriptive encoding. Moreover, VecKM is efficient to compute and scalable to large point cloud inputs: VecKM reduces the memory cost from (n2+nKd) to (nd+np); and reduces the major runtime cost from computing nK MLPs to n MLPs, where n is the size of the point cloud, K is the neighborhood size, d is the encoding dimension, and p is a marginal factor. The efficiency is due to VecKM's unique factorizable property that eliminates the need of explicitly grouping points into neighbors. In the normal estimation task, VecKM demonstrates not only 100x faster inference speed but also highest accuracy and strongest robustness. In classification and segmentation tasks, integrating VecKM as a preprocessing module achieves consistently better performance than the PointNet, PointNet++, and point transformer baselines, and runs consistently faster by up to 10 times.