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This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (

We present two improvements for laser-based forest inventory. The first improvement is based on using last pulse data for tree detection. When trees overlap, the surface model between the trees corresponding to the first pulse stays high, whereas the corresponding model from the last pulse results in a drop in elevation, due to its better penetration between the trees. This drop in elevation can be used for separating trees. In a test carried out in Evo, Southern Finland, we used 292 forests plots consisting of more than 5,500 trees and airborne laser scanning (ALS) data comprised of 12.7 emitted laser pulses per m^{2}. With last pulse data, an improvement of 6% for individual tree detection was obtained when compared to using first pulse data. The improvement increased with an increasing number of stems per plot and with decreasing diameter breast height (DBH). The results confirm that there is also substantial information for tree detection in last pulse data. The second improvement is based on the use of individual tree-based features in addition to the statistical point height metrics in area-based prediction of forest variables. The commonly-used ALS point height metrics and individual tree-based features were fused into the non-parametric estimation of forest variables. By using only four individual tree-based features, stem volume estimation improved when compared to the use of statistical point height metrics. For DBH estimation, the point height metrics and individual tree-based features complemented each other. Predictions were validated at plot level.

Trees are important for the carbon balance of the Earth. Forests have great economic and ecological importance. In Finland, about 77% of the country’s land area is forested, which is the highest percentage in Europe. International interest in biomass detection is strongly linked to forest health, photosynthetic activity and other processes related to the carbon cycle [

Approaches aimed at obtaining forest and forestry data from airborne laser scanning (ALS) data have been divided into two groups [

Initially, ITD began with the manual interpretation of analogue aerial images [

The ABA has been performed with statistical metrics, calculated from a point cloud, and ITD has been done using the dimensions of the detected trees. However, the methods have been converged for a long time (e.g., [

Conventionally, trees are detected from CHMs, which are interpolated from the point data [

The boreal managed forest study area, 5 × 5 km in size, is situated in Evo, Southern Finland. A total of 5,532 trees from 292 plots, each with a radius of 10 m, were used. The plots were measured in 2009. The average stand size in the study area is slightly less than 1 ha. The terrain elevation varies between 125 m and 185 m above sea level. Scots Pine (

The ALS data were collected in the summer of 2009 using a Leica ALS50-II system operating at a pulse rate of 150 kHz. The data were acquired using a flight altitude of 400 m with FOV of 30 degrees. ALS data comprised of 12.7 emitted laser pulses per m^{2}, including overlaps of strips. A footprint of 8.8 cm in diameter, collected by a beam having a divergence of 0.22 mrad, was achieved. The system was configured to record multiple returns per pulse,

The ground points were classified using TerraScan and based on the method explained in [

Most of the current approaches for tree detection are based on finding trees from the CHM, which is calculated as a maximum of canopy height values within each raster cell. Thus, the CHM corresponds to the maximum canopy height of the first pulse data. Our approach is based on using the canopy penetration capability of the last pulse returns with overlapping trees. When trees overlap, the surface model corresponding to the first pulse stays high, whereas with last pulse, even a small gap results in a drop in elevation,

The comparison consisted of the following steps:

Different raster models with 0.5 m × 0.5 m pixel size were created for tree location. The created models were as follows: minimum of last returns (Lmin), maximum of last returns (Lmax), mean of last returns (Lmean), and first returns maximum (Fmax).

The raster models were smoothed by means of a Gaussian filter. A 3 m × 3 m window size was selected in order to eliminate minor tree level fluctuations and to avoid the merging of overlapping trees. Given Finland’s forest conditions, larger window sizes lead to the merging of overlapping trees, especially when trying to locate trees from within the suppressed tree storey.

Local maxima were sought from the smoothed surface model in a 3 m × 3 m window, and trees were considered to have been detected if the local maxima were greater than 2 m above the ground.

The extracted tree locations were compared with the tree locations measured in the field. The laser-detected trees were automatically matched with trees measured in the field, based on the Hausdorff distance on XY plane. The matching technique is described in detail in [

The methodology and the applied automatic accuracy assessment are further demonstrated in

In order to demonstrate the usefulness of individual tree features in area-based predictions, which was the second objective of this paper, individual trees were located from the CHM (Fmax model), based on a method employing the minimum curvature object detection [

Plotwise mean height and the mean DBH value were obtained from the arithmetic mean values of the extracted individual tree heights and DBH. The volumes were obtained by summing up the individual tree volumes calculated from Laasasenaho’s equations [

^{2} reported in [

The results confirm that there is also substantial information for tree detection in last pulse data. Currently, in raster-based processing, this information has been largely neglected. The obtained results would even suggest the use of last pulse data for detection, but we assume that a hybrid model utilizing both the first and last pulse data should be developed, even when processing is done at raster level. The advantages of first pulse data obviously include the lower number of commission errors and the high quality of tree separation when the crowns are not overlapping, whereas the advantage of last pulse is in the separation of trees whose crowns overlap. A hybrid model, utilizing the advantages of both pulse types should be developed.

Previously, last pulse data has been demonstrated to be usable for various applications. Liang

With leaf-off data, more complex decision rules have to be developed for tree detection. With leaf-off data, the coniferous trees behave similarly to the leaf-on data, but the response of the deciduous trees can vary and needs to be studied in detail. A hybrid technique, utilizing both the first and last pulse data, may provide a working solution for deciduous canopies.

The applied 2.5 m maximum distance for tree matching is a possible error source when matching small trees. A variable distance, based on tree height, could be used in future. Matching using variable distance based on the DBH of the tree is reported in [

We wanted to show that the use of individual tree features as predictors increases the accuracy of stem volume in area-based predictions.

Individual tree-based features improved the ABA’s accuracy since they had very high correlation, e.g., with the reference stem volume. When calculating the importance of the features, most of the individual tree-based features were among the best features.

Another matter of concern is pulse density. It is probable that individual tree-based features lose some of their explanatory powers when applied at lower pulse densities, and with point densities of about 1 point/m^{2}, the improvement is assumed to be more modest. However, in [

Several ALS inventory studies have been carried out in the same Evo area as the present study. In [

Future studies should test the sensitivity of individual tree algorithms in tree finding and the sensitivity of point density for the estimation of forest variables. Since the overall estimation methods based on RF are robust, our preliminary understanding is that estimation is not as sensitive to the tree finding algorithm as has previously been reported in ITD literature. It should be borne in mind that the applied tree extraction method, namely the minimum curvature objector detection method [^{2}).

This paper reports two improvements for laser-based forest inventory. The first improvement is based on using the last returns for discriminating between overlapping trees. Using last pulse data and the test, which included 292 forests plots and more than 5,500 trees, an improvement of 6% for individual tree detection was obtained when compared to using first pulse data. In the 5–10 cm diameter breast height class, the use of last pulse resulted in a 10% better detection of trees than when using first pulse data. The results confirm that there is substantial information for tree detection in last pulse data, which should not be neglected even when using raster-based processing.

The second improvement is based on the use of individual tree-based features, in addition to statistical point height metrics, in the area-based prediction of forest variables. By using individual tree-based features as the input in non-parametric estimation, the root mean squared error, when compared to solely point height metrics, were reduced from about 25% to 20% at plot level. Point height metrics and individual tree-based features complemented each other in basal area estimation. The results confirmed the high usability of individual tree level features in the area-based estimation of forest variables.

The Academy of Finland is acknowledged for its financial support in the form of the projects “Science and Technology Towards Precision Forestry” and “Towards Improved Characterization of Map Objects”.

Four raster models for one example plot (radius 10 m) with the detected trees marked as ‘+’ and the field-measured trees marked as ‘o’. The trees designated by A, B, C and D were detectable on the Lmin image but not on the Fmax image. Lmin refers to the minimum of last returns, Lmax to the maximum of last returns, Lmean to the mean of last returns and Fmax to the first returns maximum. The return height is color coded.

The percentage of correctly matched trees when tested with 5,532 trees surveyed in the field.

The percentage of correctly matched trees as a function of plot density when tested with 5,532 trees surveyed in the field. The number of trees refers to a plot with a radius of 10 m.

The percentage of commission errors for different surface models when using the local maximum finding as the tree detection algorithm.

The percentage of correctly matched trees as a function of diameter breast height (DBH).

The feature importance (in the left column) and a scatter plot of the predicted

Descriptive statistics of the field plots accessed in the study.

^{3}/ha | |||
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Minimum | 3.9 | 7.6 | 0.4 |

Maximum | 31.7 | 50.8 | 586.2 |

Mean | 18.0 | 18.3 | 148.2 |

Standard deviation | 6.1 | 6.9 | 110.7 |

The features used in predicting the forest attributes.

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1 | meanH | Mean canopy height calculated as the arithmetic mean of the heights from the point cloud |

2 | stdH | Standard deviations of heights from the point cloud |

3 | P | Penetration calculated as a proportion of ground returns to total returns |

4 | COV | Coefficient of variation |

5 | H10 | 10^{th} percentile of canopy height distribution |

6 | H20 | 20^{th} percentile of canopy height distribution |

7 | H30 | 30^{th} percentile of canopy height distribution |

8 | H40 | 40^{th} percentile of canopy height distribution |

9 | H50 | 50^{th} percentile of canopy height distribution |

10 | H60 | 60^{th} percentile of canopy height distribution |

11 | H70 | 70^{th} percentile of canopy height distribution |

12 | H80 | 80^{th} percentile of canopy height distribution |

13 | H90 | 90^{th} percentile of canopy height distribution |

14 | maxH | Maximum height |

15 | D10 | 10^{th} canopy cover percentile computed as the proportion of returns below 10% of the total height |

16 | D20 | 20^{th} canopy cover percentile computed as the proportion of returns below 20% of the total height |

17 | D30 | 30^{th} canopy cover percentile computed as the proportion of returns below 30% of the total height |

18 | D40 | 40^{th} canopy cover percentile computed as the proportion of returns below 40% of the total height |

19 | D50 | 50^{th} canopy cover percentile computed as the proportion of returns below 50% of the total height |

20 | D60 | 60^{th} canopy cover percentile computed as the proportion of returns below 60% of the total height |

21 | D70 | 70^{th} canopy cover percentile computed as the proportion of returns below 70% of the total height |

22 | D80 | 80^{th} canopy cover percentile computed as the proportion of returns below 80% of the total height |

23 | D90 | 90^{th} canopy cover percentile computed as the proportion of returns below 90% of the total height |

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24 | LH | Mean height of all extracted trees |

25 | LD | Mean DBH of all detected trees, derived from the extracted heights and crown areas |

26 | LB | Basal area of the plot, derived from the extracted DBH |

27 | LV | Volume of the plot, derived from the extracted DBH and height |

The bias, RMSE, and correlation coefficient (R) between the predicted and observed values were calculated as measures of the accuracy of area-based inventory based on three different feature sets.

With all features | ||||

Mean height (m) | −0.00 | 1.10 | 6.15 | 0.98 |

Mean DBH (cm) | 0.00 | 2.91 | 16.07 | 0.89 |

Volume (m^{3}/ha) |
0.24 | 30.05 | 20.32 | 0.96 |

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With point height metrics | ||||

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Mean height (m) | −0.03 | 1.25 | 6.99 | 0.98 |

Mean DBH (cm) | 0.02 | 3.02 | 16.65 | 0.88 |

Volume (m^{3}/ha) |
0.13 | 37.56 | 25.41 | 0.93 |

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Individual tree-based features | ||||

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Mean height (m) | −0.00 | 1.24 | 6.97 | 0.98 |

Mean DBH (cm) | −0.06 | 3. 54 | 19.54 | 0.83 |

Volume (m^{3}/ha) |
−1.06 | 30.16 | 20.40 | 0.96 |