# Deep Parametric Continuous Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2101.06742 · HTML: https://mlsanity.com/paper/2101.06742/

## Key facts

- Cited by 161 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 32 references that are in the map.
- First posted on arXiv 17 Jan 2021.

## Builds on (most cited first, 23 of 23)

- [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)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [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)
- [Gated Graph Sequence Neural Networks](https://mlsanity.com/paper/1511.05493/) (2015)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Multi-view Convolutional Neural Networks for 3D Shape Recognition](https://mlsanity.com/paper/1505.00880/) (2015)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [OctNet: Learning Deep 3D Representations at High Resolutions](https://mlsanity.com/paper/1611.05009/) (2016)
- [Dynamic Filter Networks](https://mlsanity.com/paper/1605.09673/) (2016)
- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [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)
- [SEGCloud: Semantic Segmentation of 3D Point Clouds](https://mlsanity.com/paper/1710.07563/) (2017)
- [Learning Rich Features from RGB-D Images for Object Detection and Segmentation](https://mlsanity.com/paper/1407.5736/) (2014)
- [Learning shape correspondence with anisotropic convolutional neural networks](https://mlsanity.com/paper/1605.06437/) (2016)
- [SyncSpecCNN: Synchronized Spectral CNN for 3D Shape Segmentation](https://mlsanity.com/paper/1612.00606/) (2016)

## Built on by (most cited first, 30 of 161)

- [Swin Transformer V2: Scaling Up Capacity and Resolution](https://mlsanity.com/paper/2111.09883/) (2021)
- [Point Transformer V3: Simpler, Faster, Stronger](https://mlsanity.com/paper/2312.10035/) (2023)
- [Point Transformer V2: Grouped Vector Attention and Partition-based Pooling](https://mlsanity.com/paper/2210.05666/) (2022)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [PAConv: Position Adaptive Convolution with Dynamic Kernel Assembling on Point Clouds](https://mlsanity.com/paper/2103.14635/) (2021)
- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [Stratified Transformer for 3D Point Cloud Segmentation](https://mlsanity.com/paper/2203.14508/) (2022)
- [InstanceRefer: Cooperative Holistic Understanding for Visual Grounding on Point Clouds through Instance Multi-level Contextual Referring](https://mlsanity.com/paper/2103.01128/) (2021)
- [RangeDet:In Defense of Range View for LiDAR-based 3D Object Detection](https://mlsanity.com/paper/2103.10039/) (2021)
- [3D Object Detection for Autonomous Driving: A Comprehensive Survey](https://mlsanity.com/paper/2206.09474/) (2022)
- [Mix3D: Out-of-Context Data Augmentation for 3D Scenes](https://mlsanity.com/paper/2110.02210/) (2021)
- [CKConv: Continuous Kernel Convolution For Sequential Data](https://mlsanity.com/paper/2102.02611/) (2021)
- [Sonata: Self-Supervised Learning of Reliable Point Representations](https://mlsanity.com/paper/2503.16429/) (2025)
- [Bidirectional Projection Network for Cross Dimension Scene Understanding](https://mlsanity.com/paper/2103.14326/) (2021)
- [Learning to Generate Realistic LiDAR Point Clouds](https://mlsanity.com/paper/2209.03954/) (2022)
- [POCO: Point Convolution for Surface Reconstruction](https://mlsanity.com/paper/2201.01831/) (2022)
- [Towards Large-scale 3D Representation Learning with Multi-dataset Point Prompt Training](https://mlsanity.com/paper/2308.09718/) (2023)
- [Surface Representation for Point Clouds](https://mlsanity.com/paper/2205.05740/) (2022)
- [PointMixer: MLP-Mixer for Point Cloud Understanding](https://mlsanity.com/paper/2111.11187/) (2021)
- [FlexConv: Continuous Kernel Convolutions with Differentiable Kernel Sizes](https://mlsanity.com/paper/2110.08059/) (2021)
- [Multi-Modal 3D Object Detection in Autonomous Driving: a Survey](https://mlsanity.com/paper/2106.12735/) (2021)
- [Neural Operators with Localized Integral and Differential Kernels](https://mlsanity.com/paper/2402.16845/) (2024)
- [Weakly Supervised Learning of Rigid 3D Scene Flow](https://mlsanity.com/paper/2102.08945/) (2021)
- [Adaptive Graph Convolution for Point Cloud Analysis](https://mlsanity.com/paper/2108.08035/) (2021)
- [PRA-Net: Point Relation-Aware Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2112.04903/) (2021)
- [A Survey on Graph Neural Networks and Graph Transformers in Computer Vision: A Task-Oriented Perspective](https://mlsanity.com/paper/2209.13232/) (2022)
- [Generative Zero-Shot Learning for Semantic Segmentation of 3D Point Clouds](https://mlsanity.com/paper/2108.06230/) (2021)
- [Learning Semantic Segmentation of Large-Scale Point Clouds with Random Sampling](https://mlsanity.com/paper/2107.02389/) (2021)
- [Scalable Scene Flow from Point Clouds in the Real World](https://mlsanity.com/paper/2103.01306/) (2021)
- [Efficient Deformable ConvNets: Rethinking Dynamic and Sparse Operator for Vision Applications](https://mlsanity.com/paper/2401.06197/) (2024)

## Abstract (arXiv)

Standard convolutional neural networks assume a grid structured input is available and exploit discrete convolutions as their fundamental building blocks. This limits their applicability to many real-world applications. In this paper we propose Parametric Continuous Convolution, a new learnable operator that operates over non-grid structured data. The key idea is to exploit parameterized kernel functions that span the full continuous vector space. This generalization allows us to learn over arbitrary data structures as long as their support relationship is computable. Our experiments show significant improvement over the state-of-the-art in point cloud segmentation of indoor and outdoor scenes, and lidar motion estimation of driving scenes.