# DeltaConv: Anisotropic Operators for Geometric Deep Learning on Point Clouds

arXiv: https://arxiv.org/abs/2111.08799 · HTML: https://mlsanity.com/paper/2111.08799/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 72 of its 112 references that are in the map.
- First posted on arXiv 16 Nov 2021.

## Builds on (most cited first, 30 of 72)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [4D Spatio-Temporal ConvNets: Minkowski Convolutional Neural Networks](https://mlsanity.com/paper/1904.08755/) (2019)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [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)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Relation-Shape Convolutional Neural Network for Point Cloud Analysis](https://mlsanity.com/paper/1904.07601/) (2019)
- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [Vector Neurons: A General Framework for SO(3)-Equivariant Networks](https://mlsanity.com/paper/2104.12229/) (2021)

## Built on by (most cited first, 10 of 10)

- [Understanding and Improving Features Learned in Deep Functional Maps](https://mlsanity.com/paper/2303.16527/) (2023)
- [A comprehensive overview of deep learning techniques for 3D point cloud classification and semantic segmentation](https://mlsanity.com/paper/2405.11903/) (2024)
- [Toward Mesh-Invariant 3D Generative Deep Learning with Geometric Measures](https://mlsanity.com/paper/2306.15762/) (2023)
- [PoissonNet: A Local-Global Approach for Learning on Surfaces](https://mlsanity.com/paper/2510.14146/) (2025)
- [Basis restricted elastic shape analysis on the space of unregistered surfaces](https://mlsanity.com/paper/2311.04382/) (2023)
- [Beyond Fixed Topologies: Unregistered Training and Comprehensive Evaluation Metrics for 3D Talking Heads](https://mlsanity.com/paper/2410.11041/) (2024)
- [Learning Hemodynamic Scalar Fields on Coronary Artery Meshes: A Benchmark of Geometric Deep Learning Models](https://mlsanity.com/paper/2501.09046/) (2025)
- [Neural Descriptors: Self-Supervised Learning of Robust Local Surface Descriptors Using Polynomial Patches](https://mlsanity.com/paper/2503.03907/) (2025)
- [Neural Particle Automata: Learning Self-Organizing Particle Dynamics](https://mlsanity.com/paper/2601.16096/) (2026)
- [3D Understanding of Deformable Linear Objects: Datasets and Transferability Benchmark](https://mlsanity.com/paper/2310.08904/) (2023)

## Abstract (arXiv)

Learning from 3D point-cloud data has rapidly gained momentum, motivated by the success of deep learning on images and the increased availability of 3D~data. In this paper, we aim to construct anisotropic convolution layers that work directly on the surface derived from a point cloud. This is challenging because of the lack of a global coordinate system for tangential directions on surfaces. We introduce DeltaConv, a convolution layer that combines geometric operators from vector calculus to enable the construction of anisotropic filters on point clouds. Because these operators are defined on scalar- and vector-fields, we separate the network into a scalar- and a vector-stream, which are connected by the operators. The vector stream enables the network to explicitly represent, evaluate, and process directional information. Our convolutions are robust and simple to implement and match or improve on state-of-the-art approaches on several benchmarks, while also speeding up training and inference.