# PointCNN: Convolution On X-Transformed Points

arXiv: https://arxiv.org/abs/1801.07791 · HTML: https://mlsanity.com/paper/1801.07791/

## Key facts

- Cited by 764 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2018.

## Built on by (most cited first, 30 of 764)

- [Point-BERT: Pre-training 3D Point Cloud Transformers with Masked Point Modeling](https://mlsanity.com/paper/2111.14819/) (2021)
- [Point Transformer V3: Simpler, Faster, Stronger](https://mlsanity.com/paper/2312.10035/) (2023)
- [3D Shape Generation and Completion through Point-Voxel Diffusion](https://mlsanity.com/paper/2104.03670/) (2021)
- [PointCLIP: Point Cloud Understanding by CLIP](https://mlsanity.com/paper/2112.02413/) (2021)
- [Masked Autoencoders for Point Cloud Self-supervised Learning](https://mlsanity.com/paper/2203.06604/) (2022)
- [PointNeXt: Revisiting PointNet++ with Improved Training and Scaling Strategies](https://mlsanity.com/paper/2206.04670/) (2022)
- [Point Transformer V2: Grouped Vector Attention and Partition-based Pooling](https://mlsanity.com/paper/2210.05666/) (2022)
- [Rethinking Network Design and Local Geometry in Point Cloud: A Simple Residual MLP Framework](https://mlsanity.com/paper/2202.07123/) (2022)
- [An End-to-End Transformer Model for 3D Object Detection](https://mlsanity.com/paper/2109.08141/) (2021)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [OpenMask3D: Open-Vocabulary 3D Instance Segmentation](https://mlsanity.com/paper/2306.13631/) (2023)
- [ULIP: Learning a Unified Representation of Language, Images, and Point Clouds for 3D Understanding](https://mlsanity.com/paper/2212.05171/) (2022)
- [Point-M2AE: Multi-scale Masked Autoencoders for Hierarchical Point Cloud Pre-training](https://mlsanity.com/paper/2205.14401/) (2022)
- [PV-RCNN++: Point-Voxel Feature Set Abstraction With Local Vector Representation for 3D Object Detection](https://mlsanity.com/paper/2102.00463/) (2021)
- [Self-Supervised Pretraining of 3D Features on any Point-Cloud](https://mlsanity.com/paper/2101.02691/) (2021)
- [PAConv: Position Adaptive Convolution with Dynamic Kernel Assembling on Point Clouds](https://mlsanity.com/paper/2103.14635/) (2021)
- [SoftGroup for 3D Instance Segmentation on Point Clouds](https://mlsanity.com/paper/2203.01509/) (2022)
- [CrossPoint: Self-Supervised Cross-Modal Contrastive Learning for 3D Point Cloud Understanding](https://mlsanity.com/paper/2203.00680/) (2022)
- [Spatio-temporal Self-Supervised Representation Learning for 3D Point Clouds](https://mlsanity.com/paper/2109.00179/) (2021)
- [Walk in the Cloud: Learning Curves for Point Clouds Shape Analysis](https://mlsanity.com/paper/2105.01288/) (2021)
- [The Values Encoded in Machine Learning Research](https://mlsanity.com/paper/2106.15590/) (2021)
- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [Stratified Transformer for 3D Point Cloud Segmentation](https://mlsanity.com/paper/2203.14508/) (2022)
- [PointMamba: A Simple State Space Model for Point Cloud Analysis](https://mlsanity.com/paper/2402.10739/) (2024)
- [Contrast with Reconstruct: Contrastive 3D Representation Learning Guided by Generative Pretraining](https://mlsanity.com/paper/2302.02318/) (2023)
- [Masked Discrimination for Self-Supervised Learning on Point Clouds](https://mlsanity.com/paper/2203.11183/) (2022)
- [Revisiting Point Cloud Shape Classification with a Simple and Effective Baseline](https://mlsanity.com/paper/2106.05304/) (2021)
- [Learning 3D Representations from 2D Pre-trained Models via Image-to-Point Masked Autoencoders](https://mlsanity.com/paper/2212.06785/) (2022)
- [GAPartNet: Cross-Category Domain-Generalizable Object Perception and Manipulation via Generalizable and Actionable Parts](https://mlsanity.com/paper/2211.05272/) (2022)

## Abstract (arXiv)

We present a simple and general framework for feature learning from point clouds. The key to the success of CNNs is the convolution operator that is capable of leveraging spatially-local correlation in data represented densely in grids (e.g. images). However, point clouds are irregular and unordered, thus directly convolving kernels against features associated with the points, will result in desertion of shape information and variance to point ordering. To address these problems, we propose to learn an X-transformation from the input points, to simultaneously promote two causes. The first is the weighting of the input features associated with the points, and the second is the permutation of the points into a latent and potentially canonical order. Element-wise product and sum operations of the typical convolution operator are subsequently applied on the X-transformed features. The proposed method is a generalization of typical CNNs to feature learning from point clouds, thus we call it PointCNN. Experiments show that PointCNN achieves on par or better performance than state-of-the-art methods on multiple challenging benchmark datasets and tasks.