# Point Cloud Denoising With Fine-Granularity Dynamic Graph Convolutional Networks

arXiv: https://arxiv.org/abs/2411.14158 · HTML: https://mlsanity.com/paper/2411.14158/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 39 of its 74 references that are in the map.
- First posted on arXiv 21 Nov 2024.

## Builds on (most cited first, 30 of 39)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learning](https://mlsanity.com/paper/1801.07606/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Representation Learning on Graphs with Jumping Knowledge Networks](https://mlsanity.com/paper/1806.03536/) (2018)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [PairNorm: Tackling Oversmoothing in GNNs](https://mlsanity.com/paper/1909.12223/) (2019)
- [Towards Deeper Graph Neural Networks](https://mlsanity.com/paper/2007.09296/) (2020)
- [GRAND: Graph Neural Diffusion](https://mlsanity.com/paper/2106.10934/) (2021)
- [A Note on Over-Smoothing for Graph Neural Networks](https://mlsanity.com/paper/2006.13318/) (2020)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [BernNet: Learning Arbitrary Graph Spectral Filters via Bernstein Approximation](https://mlsanity.com/paper/2106.10994/) (2021)
- [Graph Neural Networks with convolutional ARMA filters](https://mlsanity.com/paper/1901.01343/) (2019)
- [Graph Neural Ordinary Differential Equations](https://mlsanity.com/paper/1911.07532/) (2019)
- [Interpreting and Unifying Graph Neural Networks with An Optimization Framework](https://mlsanity.com/paper/2101.11859/) (2021)
- [Continuous Graph Neural Networks](https://mlsanity.com/paper/1912.00967/) (2019)
- [PointCleanNet: Learning to Denoise and Remove Outliers from Dense Point Clouds](https://mlsanity.com/paper/1901.01060/) (2019)
- [PCPNET: Learning Local Shape Properties from Raw Point Clouds](https://mlsanity.com/paper/1710.04954/) (2017)
- [Beltrami Flow and Neural Diffusion on Graphs](https://mlsanity.com/paper/2110.09443/) (2021)
- [LanczosNet: Multi-Scale Deep Graph Convolutional Networks](https://mlsanity.com/paper/1901.01484/) (2019)
- [Understanding convolution on graphs via energies](https://mlsanity.com/paper/2206.10991/) (2022)

## Built on by (most cited first, 1 of 1)

- [Deep Learning For Point Cloud Denoising: A Survey](https://mlsanity.com/paper/2508.11932/) (2025)

## Abstract (arXiv)

Due to limitations in acquisition equipment, noise perturbations often corrupt 3-D point clouds, hindering down-stream tasks such as surface reconstruction, rendering, and further processing. Existing 3-D point cloud denoising methods typically fail to reliably fit the underlying continuous surface, resulting in a degradation of reconstruction performance. This paper introduces fine-granularity dynamic graph convolutional networks called GD-GCN, a novel approach to denoising in 3-D point clouds. The GD-GCN employs micro-step temporal graph convolution (MST-GConv) to perform feature learning in a gradual manner. Compared with the conventional GCN, which commonly uses discrete integer-step graph convolution, this modification introduces a more adaptable and nuanced approach to feature learning within graph convolution networks. It more accurately depicts the process of fitting the point cloud with noise to the underlying surface by and the learning process for MST-GConv acts like a changing system and is managed through a type of neural network known as neural Partial Differential Equations (PDEs). This means it can adapt and improve over time. GD-GCN approximates the Riemannian metric, calculating distances between points along a low-dimensional manifold. This capability allows it to understand the local geometric structure and effectively capture diverse relationships between points from different geometric regions through geometric graph construction based on Riemannian distances. Additionally, GD-GCN incorporates robust graph spectral filters based on the Bernstein polynomial approximation, which modulate eigenvalues for complex and arbitrary spectral responses, providing theoretical guarantees for BIBO stability. Symmetric channel mixing matrices further enhance filter flexibility by enabling channel-level scaling and shifting in the spectral domain.