# Graph-Based Depth Denoising & Dequantization for Point Cloud Enhancement

arXiv: https://arxiv.org/abs/2111.04946 · HTML: https://mlsanity.com/paper/2111.04946/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 89 references that are in the map.
- First posted on arXiv 9 Nov 2021.

## Builds on (most cited first, 14 of 14)

- [A Large Dataset to Train Convolutional Networks for Disparity, Optical Flow, and Scene Flow Estimation](https://mlsanity.com/paper/1512.02134/) (2015)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [PointCleanNet: Learning to Denoise and Remove Outliers from Dense Point Clouds](https://mlsanity.com/paper/1901.01060/) (2019)
- [Point Cloud Quality Assessment: Dataset Construction and Learning-based No-Reference Metric](https://mlsanity.com/paper/2012.11895/) (2020)
- [Differentiable Manifold Reconstruction for Point Cloud Denoising](https://mlsanity.com/paper/2007.13551/) (2020)
- [3D Point Cloud Denoising using Graph Laplacian Regularization of a Low Dimensional Manifold Model](https://mlsanity.com/paper/1803.07252/) (2018)
- [Feature Graph Learning for 3D Point Cloud Denoising](https://mlsanity.com/paper/1907.09138/) (2019)
- [Graph-Based Blind Image Deblurring From a Single Photograph](https://mlsanity.com/paper/1802.07929/) (2018)
- [Deep Graph Laplacian Regularization for Robust Denoising of Real Images](https://mlsanity.com/paper/1807.11637/) (2018)
- [Fast 3D Point Cloud Denoising via Bipartite Graph Approximation & Total Variation](https://mlsanity.com/paper/1804.10831/) (2018)
- [Precision Enhancement of 3D Surfaces from Multiple Compressed Depth Maps](https://mlsanity.com/paper/1405.2062/) (2014)
- [3D Point Cloud Enhancement using Graph-Modelled Multiview Depth Measurements](https://mlsanity.com/paper/2002.04537/) (2020)

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

- [Consistent Time-of-Flight Depth Denoising via Graph-Informed Geometric Attention](https://mlsanity.com/paper/2506.23542/) (2025)

## Abstract (arXiv)

A 3D point cloud is typically constructed from depth measurements acquired by sensors at one or more viewpoints. The measurements suffer from both quantization and noise corruption. To improve quality, previous works denoise a point cloud textita posteriori after projecting the imperfect depth data onto 3D space. Instead, we enhance depth measurements directly on the sensed images textita priori, before synthesizing a 3D point cloud. By enhancing near the physical sensing process, we tailor our optimization to our depth formation model before subsequent processing steps that obscure measurement errors. Specifically, we model depth formation as a combined process of signal-dependent noise addition and non-uniform log-based quantization. The designed model is validated (with parameters fitted) using collected empirical data from a representative depth sensor. To enhance each pixel row in a depth image, we first encode intra-view similarities between available row pixels as edge weights via feature graph learning. We next establish inter-view similarities with another rectified depth image via viewpoint mapping and sparse linear interpolation. This leads to a maximum a posteriori (MAP) graph filtering objective that is convex and differentiable. We minimize the objective efficiently using accelerated gradient descent (AGD), where the optimal step size is approximated via Gershgorin circle theorem (GCT). Experiments show that our method significantly outperformed recent point cloud denoising schemes and state-of-the-art image denoising schemes in two established point cloud quality metrics.