# Potential Convolution: Embedding Point Clouds into Potential Fields

arXiv: https://arxiv.org/abs/2104.01754 · HTML: https://mlsanity.com/paper/2104.01754/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 35 of its 53 references that are in the map.
- First posted on arXiv 5 Apr 2021.

## Builds on (most cited first, 30 of 35)

- [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)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [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)
- [3D Semantic Segmentation with Submanifold Sparse Convolutional Networks](https://mlsanity.com/paper/1711.10275/) (2017)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [Large-scale Point Cloud Semantic Segmentation with Superpoint Graphs](https://mlsanity.com/paper/1711.09869/) (2017)
- [OctNet: Learning Deep 3D Representations at High Resolutions](https://mlsanity.com/paper/1611.05009/) (2016)
- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [SpiderCNN: Deep Learning on Point Sets with Parameterized Convolutional Filters](https://mlsanity.com/paper/1803.11527/) (2018)
- [Volumetric and Multi-View CNNs for Object Classification on 3D Data](https://mlsanity.com/paper/1604.03265/) (2016)
- [Submanifold Sparse Convolutional Networks](https://mlsanity.com/paper/1706.01307/) (2017)
- [SO-Net: Self-Organizing Network for Point Cloud Analysis](https://mlsanity.com/paper/1803.04249/) (2018)
- [SEGCloud: Semantic Segmentation of 3D Point Clouds](https://mlsanity.com/paper/1710.07563/) (2017)
- [Tangent Convolutions for Dense Prediction in 3D](https://mlsanity.com/paper/1807.02443/) (2018)
- [SGPN: Similarity Group Proposal Network for 3D Point Cloud Instance Segmentation](https://mlsanity.com/paper/1711.08588/) (2017)
- [Deep Parametric Continuous Convolutional Neural Networks](https://mlsanity.com/paper/2101.06742/) (2021)
- [Semantic3D.net: A new Large-scale Point Cloud Classification Benchmark](https://mlsanity.com/paper/1704.03847/) (2017)
- [SPLATNet: Sparse Lattice Networks for Point Cloud Processing](https://mlsanity.com/paper/1802.08275/) (2018)
- [Point Convolutional Neural Networks by Extension Operators](https://mlsanity.com/paper/1803.10091/) (2018)
- [Escape from Cells: Deep Kd-Networks for the Recognition of 3D Point Cloud Models](https://mlsanity.com/paper/1704.01222/) (2017)
- [Pointwise Convolutional Neural Networks](https://mlsanity.com/paper/1712.05245/) (2017)
- [ShellNet: Efficient Point Cloud Convolutional Neural Networks using Concentric Shells Statistics](https://mlsanity.com/paper/1908.06295/) (2019)
- [Deep Projective 3D Semantic Segmentation](https://mlsanity.com/paper/1705.03428/) (2017)
- [SyncSpecCNN: Synchronized Spectral CNN for 3D Shape Segmentation](https://mlsanity.com/paper/1612.00606/) (2016)
- [Monte Carlo Convolution for Learning on Non-Uniformly Sampled Point Clouds](https://mlsanity.com/paper/1806.01759/) (2018)
- [ConvPoint: Continuous Convolutions for Point Cloud Processing](https://mlsanity.com/paper/1904.02375/) (2019)

## Abstract (arXiv)

Recently, various convolutions based on continuous or discrete kernels for point cloud processing have been widely studied, and achieve impressive performance in many applications, such as shape classification, scene segmentation and so on. However, they still suffer from some drawbacks. For continuous kernels, the inaccurate estimation of the kernel weights constitutes a bottleneck for further improving the performance; while for discrete ones, the kernels represented as the points located in the 3D space are lack of rich geometry information. In this work, rather than defining a continuous or discrete kernel, we directly embed convolutional kernels into the learnable potential fields, giving rise to potential convolution. It is convenient for us to define various potential functions for potential convolution which can generalize well to a wide range of tasks. Specifically, we provide two simple yet effective potential functions via point-wise convolution operations. Comprehensive experiments demonstrate the effectiveness of our method, which achieves superior performance on the popular 3D shape classification and scene segmentation benchmarks compared with other state-of-the-art point convolution methods.