# Continuous Conditional Random Field Convolution for Point Cloud Segmentation

arXiv: https://arxiv.org/abs/2110.06085 · HTML: https://mlsanity.com/paper/2110.06085/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 64 references that are in the map.
- First posted on arXiv 12 Oct 2021.

## Builds on (most cited first, 30 of 41)

- [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)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [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)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [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)
- [KPConv: Flexible and Deformable Convolution for Point Clouds](https://mlsanity.com/paper/1904.08889/) (2019)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [PointConv: Deep Convolutional Networks on 3D Point Clouds](https://mlsanity.com/paper/1811.07246/) (2018)
- [RandLA-Net: Efficient Semantic Segmentation of Large-Scale Point Clouds](https://mlsanity.com/paper/1911.11236/) (2019)
- [Deep Learning for 3D Point Clouds: A Survey](https://mlsanity.com/paper/1912.12033/) (2019)
- [DeepGCNs: Can GCNs Go as Deep as CNNs?](https://mlsanity.com/paper/1904.03751/) (2019)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Large-scale Point Cloud Semantic Segmentation with Superpoint Graphs](https://mlsanity.com/paper/1711.09869/) (2017)
- [Relation-Shape Convolutional Neural Network for Point Cloud Analysis](https://mlsanity.com/paper/1904.07601/) (2019)
- [OctNet: Learning Deep 3D Representations at High Resolutions](https://mlsanity.com/paper/1611.05009/) (2016)
- [SpiderCNN: Deep Learning on Point Sets with Parameterized Convolutional Filters](https://mlsanity.com/paper/1803.11527/) (2018)
- [PointASNL: Robust Point Clouds Processing using Nonlocal Neural Networks with Adaptive Sampling](https://mlsanity.com/paper/2003.00492/) (2020)
- [SqueezeSeg: Convolutional Neural Nets with Recurrent CRF for Real-Time Road-Object Segmentation from 3D LiDAR Point Cloud](https://mlsanity.com/paper/1710.07368/) (2017)
- [Conditional Random Fields as Recurrent Neural Networks](https://mlsanity.com/paper/1502.03240/) (2015)
- [PAConv: Position Adaptive Convolution with Dynamic Kernel Assembling on Point Clouds](https://mlsanity.com/paper/2103.14635/) (2021)
- [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)

## Built on by (most cited first, 7 of 7)

- [Gaussian Splatting with NeRF-based Color and Opacity](https://mlsanity.com/paper/2312.13729/) (2023)
- [Points2NeRF: Generating Neural Radiance Fields from 3D point cloud](https://mlsanity.com/paper/2206.01290/) (2022)
- [HyperNeRFGAN: Hypernetwork approach to 3D NeRF GAN](https://mlsanity.com/paper/2301.11631/) (2023)
- [MultiPlaneNeRF: Neural Radiance Field with Non-Trainable Representation](https://mlsanity.com/paper/2305.10579/) (2023)
- [NeRFlame: FLAME-based conditioning of NeRF for 3D face rendering](https://mlsanity.com/paper/2303.06226/) (2023)
- [HyperPlanes: Hypernetwork Approach to Rapid NeRF Adaptation](https://mlsanity.com/paper/2402.01524/) (2024)
- [Multi-view Structural Convolution Network for Domain-Invariant Point Cloud Recognition of Autonomous Vehicles](https://mlsanity.com/paper/2501.16289/) (2025)

## Abstract (arXiv)

Point cloud segmentation is the foundation of 3D environmental perception for modern intelligent systems. To solve this problem and image segmentation, conditional random fields (CRFs) are usually formulated as discrete models in label space to encourage label consistency, which is actually a kind of postprocessing. In this paper, we reconsider the CRF in feature space for point cloud segmentation because it can capture the structure of features well to improve the representation ability of features rather than simply smoothing. Therefore, we first model the point cloud features with a continuous quadratic energy model and formulate its solution process as a message-passing graph convolution, by which it can be easily integrated into a deep network. We theoretically demonstrate that the message passing in the graph convolution is equivalent to the mean-field approximation of a continuous CRF model. Furthermore, we build an encoder-decoder network based on the proposed continuous CRF graph convolution (CRFConv), in which the CRFConv embedded in the decoding layers can restore the details of high-level features that were lost in the encoding stage to enhance the location ability of the network, thereby benefiting segmentation. Analogous to the CRFConv, we show that the classical discrete CRF can also work collaboratively with the proposed network via another graph convolution to further improve the segmentation results. Experiments on various point cloud benchmarks demonstrate the effectiveness and robustness of the proposed method. Compared with the state-of-the-art methods, the proposed method can also achieve competitive segmentation performance.