# Retrieval of Forest Vertical Structure from PolInSAR Data by Machine Learning Using LIDAR-Derived Features

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## Abstract

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## 1. Introduction

- Viewing geometry: the LIDAR has a near vertical illumination around nadir while the radar has a slanted side-view geometry.
- Wavelength: The radar operates at wavelengths on the order of several centimeters, being sensitive to larger canopy components with variations in moisture changing the dielectric constant of plants. The UAVSAR operates at 23.8 cm penetrating the forest canopy. The LVIS LIDAR operates at 1064 nm and is reflected by all intercepted surfaces including leaves and branches.

## 2. The PolInSAR Information

#### 2.1. PolInSAR Parameters

#### 2.2. The Coherence Region

- a single point, or a line segment,
- an ellipse,
- a triangle, the convex hull of the three eigenvalues,
- an ovular shape, as represented in Figure 2 on the left,
- the union of one point and an ellipse. One of the points and the foci of the ellipse are eigenvalues of A (center panel of Figure 2),
- an ovular shape with a flat portion parallel to the imaginary axis (right panel of Figure 2).

#### 2.3. Factors That Impact the Shape of the Coherence Region

#### Geometry of Acquisition

#### 2.4. Coherence Region Parameters

- three parameters describing the position and orientation of the coherence shape: ${\rho}_{\mathrm{mean}}$, ${\theta}_{\mathrm{mean}}{h}_{a}/2\pi $, and $\alpha {h}_{a}/2\pi $,
- two describing the dimensions of the closest ellipse ${\lambda}_{min}$ and ${\lambda}_{max}$
- two parameters ${\mathrm{R}}_{\mathrm{p}}$ and ${\mathrm{R}}_{\mathrm{a}}$ describing the similarity of the observed coherence shape and theoretical ellipse.

## 3. LIDAR Processing

#### 3.1. Tree Height

#### 3.2. Canopy Cover

#### 3.3. Vertical Distribution Complexity

## 4. Fusion with Machine Learning

#### 4.1. Neural Networks

- Perceptrons are easy to implement, run fast with only a few tuning parameters and also provide a classification score.
- The mapping of PolInSAR parameters into LIDAR labels cannot be represented as a simple function. Although, SVMs have been used in similar approaches with encouraging results [35], we obtained higher accuracy with neural networks.
- A significant practical advantage of a perceptron over SVMs is that perceptrons can be trained on-line, with their weights updated as new examples are provided. Thus, perceptrons are well adapted in the context of constant renewal of remote sensing data.

#### 4.2. Random Forests

#### 4.3. The Data Set

#### 4.4. The Training Set

## 5. Results

#### 5.1. Tree Height

#### 5.2. Canopy Cover

#### 5.3. CHP Class

#### 5.4. Difficulties and Limits

#### 5.4.1. Concerning RH100

#### 5.4.2. Concerning Canopy Cover

#### 5.4.3. Concerning Vegetation Class

#### 5.5. Upscaling

## 6. Summary and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Examples of three types of coherence shape: ovular shape, union of ellipse and one point, ovular shape with flat portion.

**Figure 3.**Example of coherence region associated with different vertical forest profiles: 9-m pine trees on the

**Top**, 12-m spruce tress on the

**Bottom**.

**Figure 5.**Visualization of the main coherence shape parameters. ${\lambda}_{1},{\lambda}_{2},{\lambda}_{3}$ are the eigen values of matrix A (see Figure 2).

**Figure 8.**Principle of the Gaussian decomposition algorithm (scheme by [29]).

**Figure 11.**Three classes of vertical distributions in Laurentides Forest obtained by a spectral clustering.

**Figure 20.**Density plot of RH100 estimated by a RVoG based inversion method VS our seven parameter machine learning-based method.

**Figure 21.**In green/brown: forest/non-forest zone.

**Top**: reference.

**bottom**: Classification done from the first computed Legendre coefficient with a perceptron.

**Figure 22.**Estimation of canopy cover.

**Top**: classification by LIDAR;

**Bottom**: classification achieved from SAR after learning.

**Figure 23.**Classification map of vertical profile classes.

**Top left**: ground truth;

**Top right**: Prediction;

**Bottom**: legend with examples of profiles corresponding to each class.

**Table 1.**Description of the selected geometrical parameters characterizing the PolInSAR coherence region.

Our 7 Features Set | Description |
---|---|

${\rho}_{\mathrm{mean}}$ | Mean absolute coherence |

${\theta}_{\mathrm{mean}}{h}_{a}/2\pi $ | Mean height center height |

$\alpha {h}_{a}/2\pi $ | Equivalent height for $\alpha $ |

${\lambda}_{\mathrm{min}}$ | Spread of the shape along the minor axis |

${\lambda}_{\mathrm{max}}$ | Spread of the shape along the major axis |

${R}_{a}$ | area ratio b/w the shape and the Closest Ellipse |

${R}_{p}$ | perimeter ratio b/w the shape and the CE |

Lexico Set | Lexico Set | Eigen Values Set | Eigen Values Set | Our 7 Features |
---|---|---|---|---|

(Cartesian) | (Polar) | (Cartesian) | (Polar) | Set |

${\gamma}_{\mathrm{x}\mathrm{Hh}}$ | ${\rho}_{\mathrm{Hh}}$ | ${\lambda}_{{1}_{X}}$ | $|{\lambda}_{1}|$ | ${\gamma}_{\mathrm{mean}}$ |

${\gamma}_{\mathrm{y}\mathrm{Hh}}$ | ${\varphi}_{\mathrm{Hh}}$ | ${\lambda}_{{1}_{Y}}$ | $pha\left({\lambda}_{1}\right)$ | ${\theta}_{\mathrm{mean}}/{k}_{z}$ |

${\gamma}_{\mathrm{x}\mathrm{Hv}}$ | ${\rho}_{\mathrm{Hv}}$ | ${\lambda}_{{2}_{X}}$ | $|{\lambda}_{2}|$ | $\alpha /{k}_{z}$ |

${\gamma}_{\mathrm{y}\mathrm{Hv}}$ | ${\varphi}_{\mathrm{Hv}}$ | ${\lambda}_{{2}_{Y}}$ | $pha\left(\right|{\lambda}_{2}\left|\right)$ | ${\lambda}_{\mathrm{max}}$ |

${\gamma}_{\mathrm{x}\mathrm{Vv}}$ | ${\rho}_{\mathrm{Vv}}$ | ${\lambda}_{{3}_{X}}$ | $|{\lambda}_{3}|$ | ${\lambda}_{\mathrm{min}}$ |

${\gamma}_{\mathrm{y}\mathrm{Vv}}$ | ${\varphi}_{\mathrm{Vv}}$ | ${\lambda}_{{3}_{Y}}$ | $pha\left(\right|{\lambda}_{3}\left|\right)$ | ${R}_{p}$ |

${k}_{z}$ | ${k}_{z}$ | ${k}_{z}$ | ${k}_{z}$ | ${R}_{a}$ |

Pauli Set | Pauli Set | Eigen Values Set | Eigen Values Set | Our 7 Features |
---|---|---|---|---|

(Cartesian) | (Polar) | (Cartesian) | (Polar) | Set |

4.3 | 4.15 | 5.0 | 3.5 | 3.2 |

Pauli Set | Pauli Set | Eigen Values Set | Eigen Values Set | Our 7 Features |
---|---|---|---|---|

(Cartesian) | (Polar) | (Cartesian) | (Polar) | Set |

51% | 42% | 25% | 13% | 14% |

Actual/Predicted | Class 1 | Class 2 | Class 3 |
---|---|---|---|

Class 1 | 300.725 | 50.085 | 100.190 |

Class 2 | 150.269 | 200.545 | 100.185 |

Class 3 | 150.281 | 50.082 | 250.637 |

Pauli Set | Pauli Set | Eigen Values Set | Eigen Values Set | Our 7 Features |
---|---|---|---|---|

(Cartesian) | (Polar) | (Cartesian) | (Polar) | Set |

0.35 | 0.35 | 0.49 | 0.55 | 0.66 |

Training Extent | 100% | 50% | 25% | 10% |

RMSE RH100 (m) | 3.2 | 3.2 | 3.5 | 3.7 |

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**MDPI and ACS Style**

Brigot, G.; Simard, M.; Colin-Koeniguer, E.; Boulch, A.
Retrieval of Forest Vertical Structure from PolInSAR Data by Machine Learning Using LIDAR-Derived Features. *Remote Sens.* **2019**, *11*, 381.
https://doi.org/10.3390/rs11040381

**AMA Style**

Brigot G, Simard M, Colin-Koeniguer E, Boulch A.
Retrieval of Forest Vertical Structure from PolInSAR Data by Machine Learning Using LIDAR-Derived Features. *Remote Sensing*. 2019; 11(4):381.
https://doi.org/10.3390/rs11040381

**Chicago/Turabian Style**

Brigot, Guillaume, Marc Simard, Elise Colin-Koeniguer, and Alexandre Boulch.
2019. "Retrieval of Forest Vertical Structure from PolInSAR Data by Machine Learning Using LIDAR-Derived Features" *Remote Sensing* 11, no. 4: 381.
https://doi.org/10.3390/rs11040381