# Cross-Correlation of Diameter Measures for the Co-Registration of Forest Inventory Plots with Airborne Laser Scanning Data

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Material

#### 2.1. Study Areas

**Table 1.**Forest statistics for the two study areas. The means ± standard deviations are on the first line, minimum–maximum values are on the second one.

Study area | Dominant height (m) | Basal area (m^{2}·ha^{−}^{1}) | Coniferous proportion weighted by basal area | Stem density (ha^{−}^{1}) | Mean diameter (cm) |
---|---|---|---|---|---|

Jura | 31.8 ± 9.2 | 0.87 ± 0.12 | 510 ± 150 | 25.8 ± 7.0 | |

n_{p}
= 139 | 13.3 − 60.5 | 0.49 − 1.0 | 110 − 1, 520 | 14.8 − 54.5 | |

Vosges | 23.9 ± 7.0 | 40.7 ± 9.2 | 0.53 ± 0.38 | 1, 990 ± 2, 900 | 20.8 ± 11.5 |

n_{p}
= 95 | 7.6 − 38.4 | 10.8 − 75.2 | 0 − 1 | 170 − 17, 700 | 2.4 − 51.5 |

#### 2.2. Airborne Laser Scanning Data

^{−}

^{1}at 500 m above the ground, with a strip overlap of 60%. The pulse frequency was 180 kHz with a scan angle of ±30 degrees. The obtained mean pulse density on the 9.2 km

^{2 }was 9.3 m

^{−}

^{2}. Pre-processing of the raw files was done by the contractor. Echoes were extracted and georeferenced with the RIEGL software suite. The resulting point cloud was classified into two classes (ground and vegetation) with TerraScan. The pulse density on the field plots ranges from 6.3 to 14.1 m

^{−}

^{2}.

^{−}

^{1}at 1500 m above the ground. The pulse frequency was 71 kHz with a scan angle of ±16 degrees. The obtained mean pulse density on the 1362 km

^{2}was 2.6 m

^{−}

^{2}. TerraScan was used for echo classification in ground and non-ground categories. The pulse density on the field plots ranges from 1.1 to 4.1 m

^{−}

^{2}.

## 3. Methods

#### 3.1. Co-Registration Algorithm

**Figure 2.**The workflow for the co-registration of a forest plot with the correlation (cor) method. For the weighted mean absolute error (wmae) method, the workflow is similar, except that the minimum value is used to select the correction offset.

**Figure 3.**The workflow applied to Plot 8 of the Jura study area. (a) The plot position according to the GNSS positioning ( tree positions with a symbol size proportional to the tree diameter, × plot center); the background is the canopy height model; (b) The correlation image ( global maximum, its 3 × 3 neighborhood and the second maximum); (c) The co-registered plot according to the (−10, −2) shift corresponding to the global maximum in the correlation image.

#### 3.2. Influence of Co-Registration on the Accuracy of Prediction Models

_{mean}. Percentiles are abbreviated as h

_{g,x}with g ∈ {s, f, l} the point group and x the percentile value. Three density metrics are considered: the proportion of points above two meters that are located below $\frac{{h}_{0.99}}{2}$, $\frac{2{h}_{0.99}}{3}$ and $\frac{5{h}_{0.99}}{6}$ with h

_{0}

_{.}

_{99}the 99

^{th}percentile of heights above two meters in each plot. They are abbreviated d

_{x}with x the ratio applied to h

_{0.99}. Two CHM metrics are added: the mean value of the CHM on the plot CHM

_{mean}and the percentage of CHM values above two meters on the plot CHM

_{>}

_{2}.

#### 3.3. Influence of Forest, Topography and ALS Data Parameters on Co-Registration

_{b}is the proportion of pixels inside the plot limits with no ALS points. It reflects the amount of smoothing required by the low pulse density. Q

_{f}is computed as the the mean absolute difference between the CHM and the canopy height model filtered by the median 3 ×3 window c, for the pixels located inside the plot limits, see Equation (3). It reflects the amount of pit-filling operated by the median filter, due to both blank pixels and low pixels inside the tree crowns.

#### 3.4. Influence of the Number of Georeferenced Trees on Co-Registration

_{t}∈ {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 24, 26, 28, 30, all} for the cor method applied to diameters and n

_{t}∈{3, 4, 5, 6} for the cor and wmae methods applied to the height data of the Vosges study area. In the case that the number of trees in the plot is smaller than n

_{t}, all trees are used to compute the tree image.

## 4. Results

#### 4.1. Co-Registration

#### 4.1.1. Operator Validation

_{f}(p = 0.078) have significantly different distributions for the “doubtful” and “non-doubtful” plots in the Vosges area. “Doubtful” plots have a lower coniferous proportion, a lower altitude and a noisier canopy height model.

#### 4.1.2. Algorithm Comparison

#### 4.1.3. Comparison of the GNSS, Algorithm and Operator Positions

**Figure 4.**Cumulative proportion of validated plots as a function of the distance in meters between the operator position and the Global Navigation Satellite System (GNSS) position or the algorithm position depending on the method used (cor correlation or wmae weighted mean absolute error), the input tree variable (diameter or height) and the number of considered trees (six or all). The curves are cropped to the distance interval 0–5 m.

**Table 2.**Statistics on the distance in meters between the GNSS and operator positions and between the operator positions and various algorithm propositions for the validated plots. On the first line is the mean ± standard deviation; on the second line are the quartiles.

GNSS | cor, Diameter, All | cor, Diameter, 6 | cor, Height, All | wmae, Height, All | ||
---|---|---|---|---|---|---|

Jura | 9.0 ± 8.7 | 3.3 ± 11.0 | 3.1 ± 10.1 | |||

4.2, 6.6, 10.7 | 0.5, 0.5, 0.71 | 0.5, 0.5, 1.1 | ||||

Vosges | 1.8 ± 2.1 | 5.4 ± 7.5 | 5.3 ± 7.0 | 5.4 ± 7.3 | 6.1 ± 7.5 | |

0, 1.5, 2.8 | 0.71, 1.0, 11.3 | 0.9, 1.1, 9.8 | 0.8, 1.1, 10.8 | 0.9, 1.4, 12.8 |

#### 4.1.4. Influence of Environmental Variables on Co-Registration Error

_{1}/max

_{2}and to the median of its 3 × 3 neighborhood max

_{1}/med

_{1}. For the Vosges study area, the co-registration error is negatively correlated with basal area, mean diameter and coniferous proportion. When the wmae method is used, the error is positively correlated with stem density and negatively with the ALS vegetation point density. In all cases, the co-registration error is correlated with the ratio of the maximum value to the value of the second maximum in the cor image (in the wmae image, it corresponds to the first and second minima).

**Table 3.**Spearman correlation coefficient ρ between forest, topographic, airborne laser scanning (ALS) and co-registration variables and co-registration error (the distance between the operator and algorithm positions for the validated plots) for different algorithm settings. Significance levels: * p < 0.05,** p< 0.01, *** p < 0.001. CHM, canopy height model.

Variable | Vosges | Jura | |||
---|---|---|---|---|---|

cor, Diameter, All | cor, Height, 6 | wmae, Height, 6 | cor, Diameter, All | ||

Dominant height | −0.25 ∗ | −0.11 | −0.28 ∗ | ||

Basal area | −0.43 ∗∗∗ | −0.40 ∗∗∗ | −0.29 ∗∗ | −0.05 | |

Stem density | 0.2 | 0.09 | 0.28 ∗∗ | 0.03 | |

Mean diameter | −0.31 ∗∗ | −0.22 ∗ | −0.31 ∗∗ | −0.04 | |

Coniferous proportion | −0.54 ∗∗∗ | −0.53 ∗∗∗ | −0.31 ∗∗ | −0.15 | |

Slope | −0.16 | −0.08 | −0.05 | 0.14 | |

Altitude | −0.12 | −0.36 ∗∗∗ | −0.37 ∗∗∗ | 0.04 | |

Pulse density | 0.08 | 0.11 | −0.06 | −0.05 | |

Ground point density | 0.18 | 0.17 | −0.02 | 0.11 | |

Vegetation point density | −0.08 | −0.21 | −0.29 ∗∗ | −0.02 | |

Points below 0.5 m density | 0.19 | 0.18 | −0.02 | 0.05 | |

CHM pit-filling | −0.03 | 0.13 | 0.06 | −0.11 | |

CHM empty pixels | 0.06 | 0.05 | 0.08 | −0.04 | |

max_{1}/max_{2} | −0.41 ∗∗∗ | −0.42 ∗∗∗ | 0.41 ∗∗∗ | −0.20 ∗ | |

max_{1}/med_{1} | 0.04 | 0.02 | −0.04 | 0.24 ∗∗ |

#### 4.1.5. Influence of the Number of Sample Trees

**Figure 5.**Cumulative proportion of validated plots as a function of the distance between the operator position and the algorithm position. Line colors refer to the sample size. Subfigure titles refer to the study area, the method used (cor correlation or wmae weighted mean absolute error) and the input tree variable (diameter or height).

^{2}.

#### 4.2. Prediction Models

_{s}

_{,}

_{0}

_{.}

_{2}, h

_{f}

_{,}

_{0}

_{.}

_{6}and CHM

_{>}

_{2}when the GNSS positions are used for the training data, h

_{f}

_{,}

_{0}

_{.}

_{8}, h

_{mean}and CHM

_{>}

_{2}with the algorithm positions and h

_{f}

_{,}

_{0}

_{.}

_{4}, d

_{0}

_{.}

_{5}and CHM

_{mean}with the operator positions. With the Vosges dataset, the selected variables are h

_{mean}, d

_{0}

_{.}

_{83}and CHM

_{>}

_{2}(GNSS), h

_{l}

_{,}

_{0}

_{.}

_{8}, d

_{0}

_{.}

_{83}and CHM

_{mean}(algorithm) and h

_{mean}, d

_{0}

_{.}

_{83}and CHM

_{>}

_{2}(operator). The mean values of the root mean square error (RMSE) of basal area prediction models obtained in 1000 ten-fold cross-validations are presented in Table 4. With the Jura dataset, the estimation of RMSE is mainly affected by the positions of the validation data. It is around 7.2 m

^{2}·ha

^{−}

^{1}with the GNSS data, 6.4 with the algorithm data and 6.0 with the operator data. With the Vosges dataset, the value of the RMSE is lower when the GNSS or operator positions are used (around 9.45) than with the algorithm positions (around 9.59), but the tendency is reversed when the algorithm positions are used for the modeling.

**Table 4.**Root mean square error of basal area prediction models (1000 repetitions of ten-fold cross-validations) depending on the plot positions used in the calibration and validation steps, for the two study areas. Units are in m

^{2}·ha

^{−}

^{1}.

Calibration | Validation (Jura) | Validation (Vosges) | |||||
---|---|---|---|---|---|---|---|

GNSS | cor, Diameter, All | Operator | GNSS | cor, Diameter, All | Operator | ||

GNSS | 7.13 | 6.49 | 6.09 | 9.46 | 9.58 | 9.42 | |

cor, Diameter, All | 7.17 | 6.44 | 6.03 | 9.72 | 9.31 | 9.62 | |

Operator | 7.34 | 6.37 | 5.88 | 9.47 | 9.60 | 9.43 |

## 5. Discussion

#### 5.1. Limitations of Reference Data

**Figure 6.**The difference between stem position and apex position in tilted trees (

**a**); The shift of the apex position of a round crown when correcting a slope (

**b**,

**c**).

#### 5.2. GNSS Accuracy in Forests

^{2}·ha

^{−}

^{1}, respectively. In the Vosges area, the values are 2.4 ± 2.5, 1.3 ± 2.0 and 2.2 ± 1.9. Surprisingly, higher errors are recorded for small basal areas, which might be due to inaccurate co-registration by the operator for stands with small trees or with a low number of trees. Errors for large basal area values are similar, but it is noteworthy that the “doubtful” plots, with potentially large errors, are not taken into account. The Scandinavian study also reported a correlation of the positioning error with basal area, whereas in both areas of the present study, no correlation was significant with any of the forest or topographic variables. This might be due to the fact that “doubtful” plots are representatives of the extreme tendencies, but missing from the analysis, and that for small distances, the error is not properly evaluated, due to approximations by the operator.

#### 5.3. Possibility of Co-Registration

^{−}

^{2}[17]. For such densities, results obtained on the Jura dataset show that co-registration performs properly. When the pulse density is lower (2–4 pulses·m

^{−}

^{2}), but the variations in the canopy height model are sufficient to produce a maximum in the correlation image, correct results can also be obtained, as shown with the Vosges dataset. With pulse densities below one pulse·m

^{−}

^{2}, which can still be used for the implementation of the ALS area-based estimation method, one could expect that the modeling of the canopy is not sufficient to reflect the height variation and that the proposed approach will fail. In the absence of a field reference for the correct positions, the operator validation relied on the possibility to visually match the field trees with the CHM, so that, in the case of the Vosges dataset, some plots with a very low density had to be removed from the analysis.

#### 5.4. Automated Co-Registration

^{−}

^{2}). This performance should yet be confirmed in the case of broadleaved forests. With the higher ALS density in the Jura area, 82% (resp. 59%) of plots are co-registered below one (resp. 0.5) meter with the correlation approach. In the case of existing field plots, the terrestrial laser scanning method requires additional fieldwork to perform the scans and also relies on tree detection in both the aerial and terrestrial laser data. A major advantage is that no information about tree positions are required.

#### 5.5. Factors Affecting the Algorithm Co-Registration Error

_{1}/med

_{1}indicates if the maximum is peak-shaped or round. Peak-shaped maxima correspond to situations where the shift associated with the global maximum is precise. In the Jura area, where the conditions are easy for co-registration, the question of error, hence, comes down to whether the proposed position is accurate or not.

_{1}/max

_{2}. This ratio can be considered as a rough indicator of the signal-to-noise ratio. When its value is close to one, there are high chances that the global maxima is only an artifact caused by the irregular shapes of trees or to a low-quality CHM.

#### 5.6. Resulting Co-Registration and Prediction Models

^{2}·ha

^{−}

^{1}. The models obtained with the GNSS or algorithm positions and validated with the operator positions have only a slightly lower accuracy (RMSE of respectively 6.09 and 6.03). However, their “apparent” error, which is obtained when calibration and validation steps are processed with the same positions, are respectively 7.13 and 6.44. Considering that the position error results in a random noise affecting the independent variables, the result of an ordinary least squares regression will be scarcely affected by the changes in ALS variables, provided that the number of plots is sufficient and that there are no outliers. Indeed, the noise will hardly modify the coefficients of the best fit, but will increase the residuals. This might explain why the calibration step is not affected by position error, whereas it is important to have precise positions for the evaluation of the prediction accuracy.

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Monnet, J.-M.; Mermin, É. Cross-Correlation of Diameter Measures for the Co-Registration of Forest Inventory Plots with Airborne Laser Scanning Data. *Forests* **2014**, *5*, 2307-2326.
https://doi.org/10.3390/f5092307

**AMA Style**

Monnet J-M, Mermin É. Cross-Correlation of Diameter Measures for the Co-Registration of Forest Inventory Plots with Airborne Laser Scanning Data. *Forests*. 2014; 5(9):2307-2326.
https://doi.org/10.3390/f5092307

**Chicago/Turabian Style**

Monnet, Jean-Matthieu, and Éric Mermin. 2014. "Cross-Correlation of Diameter Measures for the Co-Registration of Forest Inventory Plots with Airborne Laser Scanning Data" *Forests* 5, no. 9: 2307-2326.
https://doi.org/10.3390/f5092307