# Feature Graph Learning for 3D Point Cloud Denoising

arXiv: https://arxiv.org/abs/1907.09138 · HTML: https://mlsanity.com/paper/1907.09138/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jul 2019.

## Built on by (most cited first, 28 of 28)

- [Score-Based Point Cloud Denoising](https://mlsanity.com/paper/2107.10981/) (2021)
- [Deep Point Set Resampling via Gradient Fields](https://mlsanity.com/paper/2111.02045/) (2021)
- [Refine-Net: Normal Refinement Neural Network for Noisy Point Clouds](https://mlsanity.com/paper/2203.12514/) (2022)
- [PD-Flow: A Point Cloud Denoising Framework with Normalizing Flows](https://mlsanity.com/paper/2203.05940/) (2022)
- [P2P-Bridge: Diffusion Bridges for 3D Point Cloud Denoising](https://mlsanity.com/paper/2408.16325/) (2024)
- [PCDNF: Revisiting Learning-based Point Cloud Denoising via Joint Normal Filtering](https://mlsanity.com/paper/2209.00798/) (2022)
- [StraightPCF: Straight Point Cloud Filtering](https://mlsanity.com/paper/2405.08322/) (2024)
- [Mask-GVAE: Blind Denoising Graphs via Partition](https://mlsanity.com/paper/2102.04228/) (2021)
- [Advancing 3D Point Cloud Understanding through Deep Transfer Learning: A Comprehensive Survey](https://mlsanity.com/paper/2407.17877/) (2024)
- [Interpretable Lightweight Transformer via Unrolling of Learned Graph Smoothness Priors](https://mlsanity.com/paper/2406.04090/) (2024)
- [MODNet: Multi-offset Point Cloud Denoising Network Customized for Multi-scale Patches](https://mlsanity.com/paper/2208.14160/) (2022)
- [Dynamic Point Cloud Denoising via Gradient Fields](https://mlsanity.com/paper/2204.08755/) (2022)
- [Rethinking Point Cloud Filtering: A Non-Local Position Based Approach](https://mlsanity.com/paper/2110.07253/) (2021)
- [NoiseTrans: Point Cloud Denoising with Transformers](https://mlsanity.com/paper/2304.11812/) (2023)
- [Graph-Based Depth Denoising & Dequantization for Point Cloud Enhancement](https://mlsanity.com/paper/2111.04946/) (2021)
- [Graph Sparsification for GCN Towards Optimal Crop Yield Predictions](https://mlsanity.com/paper/2306.01725/) (2023)
- [Signal Processing in the Retina: Interpretable Graph Classifier to Predict Ganglion Cell Responses](https://mlsanity.com/paper/2401.01813/) (2024)
- [A Radiometric Correction based Optical Modeling Approach to Removing Reflection Noise in TLS Point Clouds of Urban Scenes](https://mlsanity.com/paper/2407.02830/) (2024)
- [Hybrid Long and Short Range Flows for Point Cloud Filtering](https://mlsanity.com/paper/2508.08542/) (2025)
- [Incomplete Gamma Kernels: Generalizing Locally Optimal Projection Operators](https://mlsanity.com/paper/2205.01087/) (2022)
- [Unsupervised Graph Spectral Feature Denoising for Crop Yield Prediction](https://mlsanity.com/paper/2208.02714/) (2022)
- [NSANet: Noise Seeking Attention Network](https://mlsanity.com/paper/2302.13392/) (2023)
- [A Lennard-Jones Layer for Distribution Normalization](https://mlsanity.com/paper/2402.03287/) (2024)
- [Noise2Score3D:Unsupervised Tweedie's Approach for Point Cloud Denoising](https://mlsanity.com/paper/2502.16826/) (2025)
- [Efficient Learning of Balanced Signed Graphs via Sparse Linear Programming](https://mlsanity.com/paper/2506.01826/) (2025)
- [Mamba Learns in Context: Structure-Aware Domain Generalization for Multi-Task Point Cloud Understanding](https://mlsanity.com/paper/2603.20739/) (2026)
- [PQDT: Pseudo-Query Dual Transformer for Robust Point Cloud Restoration](https://mlsanity.com/paper/2605.25127/) (2026)
- [Graph Learning with Spectral Connectivity Priors for Scarce Data](https://mlsanity.com/paper/2609.27278/) (2026)

## Abstract (arXiv)

Identifying an appropriate underlying graph kernel that reflects pairwise similarities is critical in many recent graph spectral signal restoration schemes, including image denoising, dequantization, and contrast enhancement. Existing graph learning algorithms compute the most likely entries of a properly defined graph Laplacian matrix L, but require a large number of signal observations z's for a stable estimate. In this work, we assume instead the availability of a relevant feature vector fi per node i, from which we compute an optimal feature graph via optimization of a feature metric. Specifically, we alternately optimize the diagonal and off-diagonal entries of a Mahalanobis distance matrix M by minimizing the graph Laplacian regularizer (GLR) ztop L z, where edge weight is wi,j = exp-(fi - fj)top M (fi - fj) , given a single observation z. We optimize diagonal entries via proximal gradient (PG), where we constrain M to be positive definite (PD) via linear inequalities derived from the Gershgorin circle theorem. To optimize off-diagonal entries, we design a block descent algorithm that iteratively optimizes one row and column of M. To keep M PD, we constrain the Schur complement of sub-matrix M2,2 of M to be PD when optimizing via PG. Our algorithm mitigates full eigen-decomposition of M, thus ensuring fast computation speed even when feature vector fi has high dimension. To validate its usefulness, we apply our feature graph learning algorithm to the problem of 3D point cloud denoising, resulting in state-of-the-art performance compared to competing schemes in extensive experiments.