# Flex-Convolution (Million-Scale Point-Cloud Learning Beyond Grid-Worlds)

arXiv: https://arxiv.org/abs/1803.07289 · HTML: https://mlsanity.com/paper/1803.07289/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2018.

## Built on by (most cited first, 23 of 23)

- [PAConv: Position Adaptive Convolution with Dynamic Kernel Assembling on Point Clouds](https://mlsanity.com/paper/2103.14635/) (2021)
- [Revisiting Point Cloud Shape Classification with a Simple and Effective Baseline](https://mlsanity.com/paper/2106.05304/) (2021)
- [Dora: Sampling and Benchmarking for 3D Shape Variational Auto-Encoders](https://mlsanity.com/paper/2412.17808/) (2024)
- [Learning Semantic Segmentation of Large-Scale Point Clouds with Random Sampling](https://mlsanity.com/paper/2107.02389/) (2021)
- [Attention-based Point Cloud Edge Sampling](https://mlsanity.com/paper/2302.14673/) (2023)
- [ASSANet: An Anisotropic Separable Set Abstraction for Efficient Point Cloud Representation Learning](https://mlsanity.com/paper/2110.10538/) (2021)
- [FD-SLAM: 3-D Reconstruction Using Features and Dense Matching](https://mlsanity.com/paper/2203.13861/) (2022)
- [Meta-Sampler: Almost-Universal yet Task-Oriented Sampling for Point Clouds](https://mlsanity.com/paper/2203.16001/) (2022)
- [Pooling Revisited: Your Receptive Field is Suboptimal](https://mlsanity.com/paper/2205.15254/) (2022)
- [Deep Semantic Graph Matching for Large-scale Outdoor Point Clouds Registration](https://mlsanity.com/paper/2308.05314/) (2023)
- [MICAS: Multi-grained In-Context Adaptive Sampling for 3D Point Cloud Processing](https://mlsanity.com/paper/2411.16773/) (2024)
- [The Devils in the Point Clouds: Studying the Robustness of Point Cloud Convolutions](https://mlsanity.com/paper/2101.07832/) (2021)
- [Viewport Prediction for Volumetric Video Streaming by Exploring Video Saliency and Trajectory Information](https://mlsanity.com/paper/2311.16462/) (2023)
- [Example-Based Sampling with Diffusion Models](https://mlsanity.com/paper/2302.05116/) (2023)
- [Hierarchical Adaptive Voxel-guided Sampling for Real-time Applications in Large-scale Point Clouds](https://mlsanity.com/paper/2305.14306/) (2023)
- [TS40K: a 3D Point Cloud Dataset of Rural Terrain and Electrical Transmission System](https://mlsanity.com/paper/2405.13989/) (2024)
- [SAMBLE: Shape-Specific Point Cloud Sampling for an Optimal Trade-Off Between Local Detail and Global Uniformity](https://mlsanity.com/paper/2504.19581/) (2025)
- [Adaptive 3D Gaussian Splatting Video Streaming: Visual Saliency-Aware Tiling and Meta-Learning-Based Bitrate Adaptation](https://mlsanity.com/paper/2507.14454/) (2025)
- [Multi-resolution deep learning pipeline for dense large scale point clouds](https://mlsanity.com/paper/2109.11311/) (2021)
- [Point Cloud Segmentation Using Sparse Temporal Local Attention](https://mlsanity.com/paper/2112.00289/) (2021)
- [Variance-Aware Weight Initialization for Point Convolutional Neural Networks](https://mlsanity.com/paper/2112.03777/) (2021)
- [Approximating Continuous Convolutions for Deep Network Compression](https://mlsanity.com/paper/2210.08951/) (2022)
- [GIBLy: Improving 3D Semantic Segmentation through an Architecture-Agnostic Lightweight Geometric Inductive Bias Layer](https://mlsanity.com/paper/2605.24243/) (2026)

## Abstract (arXiv)

Traditional convolution layers are specifically designed to exploit the natural data representation of images -- a fixed and regular grid. However, unstructured data like 3D point clouds containing irregular neighborhoods constantly breaks the grid-based data assumption. Therefore applying best-practices and design choices from 2D-image learning methods towards processing point clouds are not readily possible. In this work, we introduce a natural generalization flex-convolution of the conventional convolution layer along with an efficient GPU implementation. We demonstrate competitive performance on rather small benchmark sets using fewer parameters and lower memory consumption and obtain significant improvements on a million-scale real-world dataset. Ours is the first which allows to efficiently process 7 million points concurrently.