# Multiscale Feature Fusion for the Multistage Denoising of Airborne Single Photon LiDAR

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## Abstract

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## 1. Introduction

- (1)
**The sparsity assumption of point cloud noise does not hold:**The noise in the LML point clouds is generally sparse, and many existing denoising algorithms have been proposed based on the sparsity assumption. However, the high photon sensitivity of SPL results in numerous noisy points. The noisy point density in the SPL point clouds far exceeds that in the LML point clouds. Therefore, it is hard to remove the noisy points in SPL using existing denoising algorithms (see the second and third rows of Figure 1).- (2)
**The noisy points cannot be identified with a clear mechanism of generation:**The noise in the LML point clouds is primarily due to low outliers generated by the multiple path errors. The low outliers can be removed by morphological opening and closing. In contrast, noisy points in the SPL point clouds are generated for various uncertain reasons, thus, it is difficult to construct a denoising model using a priori knowledge-based method [13].

## 2. Related Work

#### 2.1. Single-Photon LiDAR

#### 2.2. Point Cloud Denoising

#### 2.3. Point Cloud Features

#### 2.3.1. Neighborhood Definition

#### 2.3.2. Feature Selection

#### 2.3.3. Multiscale Construction

## 3. Methodology

#### 3.1. Architecture Overview

#### 3.2. Multiscale Hybrid Features of Single-Photon LiDAR

#### 3.2.1. Point-Wise Features

**Intensity-based features**: The intensity values reflect the intensity of the reflected signals by the object being measured. The intensity values can distinguish some noisy points from building points, since the intensity of some background noisy points is much lower than that of building points (Figure 3d).**Echo-based features**: N and ${N}_{e}$ can describe the echo-based features, where N represents the total number of echoes contained in the current pulse and ${N}_{e}$ stands for the normalized number of echoes. Echo-based features can initially extract the vegetation points, since there may be multiple echoes from the same pulse in the vegetation areas (Figure 3e).

#### 3.2.2. Neighborhood-Wise Features

**Height-based features**predominantly include height difference (${\mathsf{\Delta}}_{z}$), height standard deviation (${\sigma}_{z}^{2}$), and normal change rate (C). The values of height-based features will be larger in vegetated areas, high noise areas, and building boundaries, where there are more undulations (Figure 3c). We can therefore use height-based features to highlight smooth areas such as ground and building roofs.**Eigenvalue-based features**are widely used for local feature extraction from point clouds, which can effectively portray the distribution of the point cloud in the neighborhood. The eigenvalue-based features are based on the covariance matrix $D\in {\mathbb{R}}^{3\times 3}$ computed within the neighborhood ${N}_{p}$ following Equation (1):$$\begin{array}{c}D={\left(\right)}^{\begin{array}{c}{p}_{1}-\overline{p}\\ \vdots \\ {p}_{n}-\overline{p}\end{array}}T\left(\right)open="["\; close="]">\begin{array}{c}{p}_{1}-\overline{p}\\ \vdots \\ {p}_{n}-\overline{p}\end{array}\end{array}$$Here, ${p}_{i}=\left(\right)open="("\; close=")">{x}_{i},{y}_{i},{z}_{i}$ is a point contained in the neighborhood ${N}_{P}$. The geometric center $\overline{p}$ can be defined by Equation (2):$$\begin{array}{c}{\displaystyle \overline{p}=\frac{1}{n}\sum _{i=1}^{n}{p}_{i}}\end{array}$$Since the covariance matrix is a symmetric positive-definite matrix, its three eigenvalues ${\lambda}_{1},{\lambda}_{2}$, and ${\lambda}_{3}$ (${\lambda}_{3}\le {\lambda}_{2}\le {\lambda}_{1}$) exist. Therefore, the eigenvalues can be used to characterize the local neighborhood shapes by calculating the eigenvalue-based features represented by Anisotropy (${A}_{\lambda}$), Planarity (${P}_{\lambda}$), Sphericity (${S}_{\lambda}$), and Linearity (${L}_{\lambda}$), according to Equations (3)–(6):$$\begin{array}{c}{A}_{\lambda}=\frac{{\lambda}_{1}-{\lambda}_{3}}{{\lambda}_{1}}\end{array}$$$$\begin{array}{c}{P}_{\lambda}=\frac{{\lambda}_{2}-{\lambda}_{3}}{{\lambda}_{1}}\end{array}$$$$\begin{array}{c}{S}_{\lambda}=\frac{{\lambda}_{3}}{{\lambda}_{1}}\end{array}$$$$\begin{array}{c}{L}_{\lambda}=\frac{{\lambda}_{1}-{\lambda}_{2}}{{\lambda}_{1}},\end{array}$$

#### 3.2.3. Multiscale Neighborhood Features

#### 3.3. Noise Removal Using Random Forests

## 4. Experiment

#### 4.1. Datasets

#### 4.2. Evaluation Metrics

#### 4.3. Comparison of Experimental Results

#### 4.3.1. Experiments in the Urban Area

#### 4.3.2. Experiments in the Suburban Area

#### 4.3.3. Experiments in the Mountain Area

#### 4.3.4. Experiments in the Water Area

#### 4.4. Result Analysis

#### 4.4.1. Analysis of Multiscale Features

#### 4.4.2. Analysis of Multistage Denoising

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The raw point clouds data from SPL and the denoising results using existing algorithms. The three images in the right hand show the profile line in the area of the red line on the left.

**Figure 2.**Structure of the proposed network. There are three main parts: neighborhood definition, a multiscale feature extraction, and a random forests module. In the neighborhood definition module, a,b…m represent different scales.

**Figure 4.**Neighborhoods at different scales. In this representation, the red star is the centroid point of the neighborhood, the blue points are the neighbors within the local neighborhood, and the black points are the outside points of the local neighborhood. In the figure, (

**a**–

**c**) represent different scales.

**Figure 5.**Experimental data distribution chart; (

**a**) overview map of Navarra, background: Google Earth; (

**b**) the mountain area of Sorlada; (

**c**) part of the urban area of Pamplona; (

**d**) part of the suburb area of Berbinzana; (

**e**) Laguna de Pitillas Lake and its vicinity.

**Figure 6.**Examples of the denoising results in the urban area. The four images in the upper right-hand corner show the profile line in the area of the red line on the left. The third row represents the profile line partial details for convenient comparison. The fourth row indicates the DSM generated by the different denoising methods. The bottom row indicates some details of the DSM to facilitate comparison.

**Figure 7.**Examples of the denoising results in the suburban area. The four images in the upper right-hand corner show the profile line in the area of the red line on the left. The third row represents the profile line partial details for convenient comparison. The fourth row indicates the DSM generated by the different denoising methods. The bottom row indicates some details of the DSM to facilitate comparison.

**Figure 8.**Examples of the denoising results in the mountain area. The four images in the upper right-hand corner show the profile line in the area of the red line on the left. The third row represents the profile line partial details for convenient comparison. The fourth row indicates the DSM generated by the different denoising methods. The bottom row indicates some details of the DSM to facilitate comparison.

**Figure 9.**Examples of the denoising results in the water area. The four images in the upper right-hand corner show the profile line in the area of the red line on the left. The third row represents the profile line partial details for convenient comparison. The fourth row indicates the DSM generated by the different denoising methods. The bottom row indicates some details of the DSM to facilitate comparison.

**Figure 10.**Analysis of single-scale and multiscale denoising results; (

**a**) overview of the urban area; (

**b**) three-dimensional view after denoising in the 5 m neighborhood; (

**c**) three-dimensional view after denoising in the 10 m neighborhood; (

**d**) raw SPL point cloud with noise; (

**e**) three-dimensional view after denoising in the 5 m and 10 m neighborhoods; (

**f**) three-dimensional view after denoising in the 5 m, 10 m, and 15 m neighborhoods.

**Figure 11.**Visualization of the effect of single-scale versus multiscale neighborhood features on denoising results on the four datasets.

**Figure 12.**Visualization of the effect of the multiple denoising in the water area using our proposed approach. (

**a**) overview of the water area; (

**b**) three-dimensional view after the first denoising; (

**c**) profile after the first denoising; (

**d**) three-dimensional view after the second denoising; (

**e**) profile after the second denoising.

Dataset Name | Navarra Dataset |
---|---|

LiDAR system | SPL100 |

Point density | 14.5 points/m${}^{2}$ |

Flight height | 4200 m (AGL) |

Field of view (FoV) | 30° |

Flight speed | 90 m/s |

Swath width | 2260 m |

Effective scan rate | 6 MHz |

Data coverage | The Navarra province of Spain |

Coordinate system | ETRS89 / UTM zone 30 N (EPSG25830) |

Methods | Recall (%) | Precision (%) | Accuracy (%) | F1-Score (%) |
---|---|---|---|---|

Radius Outlier Removal | 82.63 | 98.51 | 93.71 | 89.87 |

Statistical Outlier Removal | 65.34 | 99.55 | 88.19 | 78.89 |

Lastools’ Denoising Workflow | 88.84 | 99.25 | 95.83 | 93.76 |

RandLA-Net | 93.98 | 94.76 | 94.07 | 94.37 |

Ours | 96.82 | 98.35 | 98.38 | 97.58 |

Methods | Recall (%) | Precision (%) | Accuracy (%) | F1-Score (%) |
---|---|---|---|---|

Radius Outlier Removal | 94.01 | 99.97 | 98.70 | 96.90 |

Statistical Outlier Removal | 93.05 | 99.99 | 98.49 | 96.39 |

Lastools’ Denoising Workflow | 88.52 | 99.98 | 97.22 | 93.91 |

RandLA-Net | 98.81 | 99.20 | 98.81 | 99.01 |

Ours | 99.86 | 99.31 | 99.82 | 99.59 |

Methods | Recall (%) | Precision (%) | Accuracy (%) | F1-Score (%) |
---|---|---|---|---|

Radius Outlier Removal | 88.86 | 99.04 | 97.46 | 93.68 |

Statistical Outlier Removal | 87.90 | 99.44 | 97.33 | 93.32 |

Lastools’ Denoising Workflow | 87.36 | 99.74 | 96.99 | 93.14 |

RandLA-Net | 96.48 | 94.26 | 96.48 | 95.35 |

Ours | 99.47 | 92.22 | 98.11 | 95.70 |

Methods | Recall (%) | Precision (%) | Accuracy (%) | F1-Score (%) |
---|---|---|---|---|

Radius Outlier Removal | 37.58 | 87.11 | 71.57 | 52.51 |

Statistical Outlier Removal | 31.19 | 98.63 | 71.04 | 47.40 |

Lastools’ Denoising Workflow | 45.74 | 98.41 | 74.19 | 62.46 |

Ours | 71.49 | 85.61 | 83.05 | 77.92 |

**Table 6.**Performance evaluation of denoising by the proposed approach, using different scales in the urban, suburban, mountain, and water areas.

Areas | Metrics | Neighborhood (m) | ||||
---|---|---|---|---|---|---|

5 | 10 | 15 | 5, 10 | 5, 10, 15 | ||

Urban | Accuracy | 96.60 | 97.15 | 97.74 | 98.04 | 98.38 |

F1-score | 94.97 | 95.72 | 96.61 | 97.08 | 97.58 | |

Mountain | Accuracy | 94.82 | 95.33 | 95.37 | 96.91 | 98.11 |

F1-score | 88.86 | 89.81 | 89.98 | 93.16 | 95.70 | |

Suburban | Accuracy | 98.54 | 98.83 | 99.27 | 99.59 | 99.82 |

F1-score | 96.70 | 97.28 | 98.31 | 99.06 | 99.59 | |

Water | Accuracy | 77.35 | 79.66 | 79.44 | 82.65 | 83.05 |

F1-score | 71.46 | 74.35 | 72.71 | 77.49 | 77.92 |

**Table 7.**Performance evaluation of denoising by multiple denoising, using different denoising approaches in the water area.

Methods | Metric | First Denoising | Second Denoising | Improvement |
---|---|---|---|---|

Radius Outlier Removal | Recall (%) | 37.58 | 38.85 | 1.27 |

Precision (%) | 87.11 | 84.12 | −2.99 | |

Accuracy (%) | 71.57 | 71.35 | −0.22 | |

F1-score (%) | 52.51 | 53.15 | 0.64 | |

Statistical Outlier Removal | Recall (%) | 31.19 | 38.05 | 6.86 |

Precision (%) | 98.63 | 94.70 | −3.93 | |

Accuracy (%) | 71.04 | 73.20 | 2.16 | |

F1-score (%) | 47.40 | 54.29 | 6.89 | |

Lastools’ Denoising Workflow | Recall (%) | 45.74 | 47.14 | 1.40 |

Precision (%) | 98.41 | 97.64 | −0.77 | |

Accuracy (%) | 74.19 | 74.66 | 0.47 | |

F1-score (%) | 62.46 | 63.58 | 1.12 | |

Ours | Recall (%) | 71.49 | 91.44 | 19.95 |

Precision (%) | 85.61 | 85.94 | 0.33 | |

Accuracy (%) | 83.05 | 90.16 | 7.11 | |

F1-score (%) | 77.92 | 88.60 | 10.68 |

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Si, S.; Hu, H.; Ding, Y.; Yuan, X.; Jiang, Y.; Jin, Y.; Ge, X.; Zhang, Y.; Chen, J.; Guo, X.
Multiscale Feature Fusion for the Multistage Denoising of Airborne Single Photon LiDAR. *Remote Sens.* **2023**, *15*, 269.
https://doi.org/10.3390/rs15010269

**AMA Style**

Si S, Hu H, Ding Y, Yuan X, Jiang Y, Jin Y, Ge X, Zhang Y, Chen J, Guo X.
Multiscale Feature Fusion for the Multistage Denoising of Airborne Single Photon LiDAR. *Remote Sensing*. 2023; 15(1):269.
https://doi.org/10.3390/rs15010269

**Chicago/Turabian Style**

Si, Shuming, Han Hu, Yulin Ding, Xuekun Yuan, Ying Jiang, Yigao Jin, Xuming Ge, Yeting Zhang, Jie Chen, and Xiaocui Guo.
2023. "Multiscale Feature Fusion for the Multistage Denoising of Airborne Single Photon LiDAR" *Remote Sensing* 15, no. 1: 269.
https://doi.org/10.3390/rs15010269