# Estimating Individual Conifer Seedling Height Using Drone-Based Image Point Clouds

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}= 0.63; n = 48) was achieved for seedlings >30 cm with 0.35 cm GSD in leaf-off conditions and ground elevation from the DIPC. The second-best result had the same GSD and ground method but was leaf-on and not significantly different from the first. Results for seedlings ≤30 cm were unreliable (nil R

^{2}). Height estimates derived from manual softcopy interpretation were similar to the corresponding DIPC results. Height estimation errors hardly affected seedling counting errors (best balance was 8% omission and 6% commission). Accuracy and correlation were stronger at finer GSDs and improved with seedling size. Conclusions: Millimetric (GSD <1 cm) DIPC can be used for estimating the height of individual conifer seedlings taller than 30 cm.

## 1. Introduction

- How accurately can conifer seedling height be estimated in drone surveys for survival (small seedlings) and establishment (older and taller seedlings)?
- Does the accuracy of DIPC differ much from that of softcopy (manual) photogrammetry?
- What is the impact of height-estimation error on counting errors in seedling surveys?
- What is the effect of spatial resolution, season, ground determination method, and seedling size on the accuracy of seedling height estimates?
- What factors contribute to outliers?

^{2}) of 0.83. A year later, Röder et al. [13] went a step further by studying individual young Norway spruce (Picea abies (L.) Karst) in eight 762-m

^{2}plots (mean tree height 1.2–4.1 m) in a conservation area in southern Germany. They obtained a mean RMSE of 1.57 m and an R

^{2}of 0.74 when comparing the DIPC-derived height (from 5 cm GSD imagery) of detected young trees with their field-measured height. In 2019, in a study of 580 circular plots (50 m

^{2}size and mean tree height 2.5 m) in regenerating stands in Norway, Puliti et al. [14] obtained an RMSE of 77 cm and an R

^{2}of 0.52. They estimated the mean tree height of these plots using a random forest model that had predictors derived from a 3 cm GSD DIPC dataset. Theirs was the first study to demonstrate that DIPC data can provide more accurate predictions than ALS (the RMSE of the best ALS model was 80 cm, even though the ALS data had a density of 5 points/m

^{2}). Also that year, Imangholiloo et al. [15] estimated the mean height of small trees within 15 plots in regenerating conifer-dominated stands in Finland (mean height 1.1–3.3 m) using 2.5 cm GSD DIPCs (both leaf off and leaf on). They obtained an RMSE of 52 cm and an R

^{2}of 0.97 with the leaf-off DIPC, and an RMSE of 27 cm and an R

^{2}of 0.95 with the leaf-on DIPC. None of these studies used a millimetric (<1 cm) GSD, and none dealt with seedlings with a mean height less than 1 m.

## 2. Materials

#### 2.1. Study Area

#### 2.2. Field Data

^{2}belt plots 75 m apart were established at opposite ends of the site. Each belt plot was further subdivided into ten 10-m

^{2}subplots. The species, height, and precise coordinates of all conifer seedlings intersecting the 150 m long site centerline were recorded, as well as those from the tallest representative seedling within each belt subplot (Figure 1).

#### 2.3. Drone Data

#### 2.3.1. Acquisition

#### 2.3.2. Drone-Based Image Point Cloud (DIPC) Generation

#### 2.3.3. Softcopy Photogrammetry

#### 2.4. Ancillary Data

^{2}with a projected vertical accuracy of 9 cm.

## 3. Methods

#### 3.1. Height Estimation

#### 3.1.1. DIPC

_{MAX}− z

_{GROUND}

_{MAX}is the elevation of the tallest DIPC point inside a vertical cylinder of 20 cm radius centered at the location, and z

_{GROUND}is the ground elevation at that location, estimated according to one of three methods described below. The 20 cm radius was found to be a good compromise between ensuring that the apex of the seedling is inside the cylinder, and avoiding the inclusion of taller points corresponding to adjacent shrubs. Any point 3 m taller than z

_{GROUND}was removed from the cylinder as it would have belonged to branches of tall neighboring trees. Several ground determination methods were tested, but after assessing preliminary results, we selected three methods for further analysis: (1) the elevation of the lowest point within a 1 m radius of the seedling location (hereafter the DIPC

_{MIN}method, which follows from Chen et al. [10]); (2) the weighed (by inverse distance) mean elevation in the 50 cm ALS DTM of the four pixel centroids nearest to the seedling location (hereafter the DTM

_{ALS}method); and (3) the weighed mean elevation of the three closest nodes in the DIPC triangular irregular network (TIN, hereafter the DIPC

_{TIN}method). The TIN was created from DIPC ground points, where the ground was classified using a method adapted from Isenburg [21] that isolates local minima and removes erroneous points depending on the minimum distance expected with no ground occlusion. Then, for each DIPC dataset and ground determination method, the predicted height of each seedling was compared with its observed (ground-measured) height (observed and predicted heights are available in Supplementary File S1). There were three GSD (0.35 cm, 0.75 cm, and 3 cm), two phenological states (leaf-on and leaf-off), and three ground determination methods (DIPC

_{MIN}, DTM

_{ALS}, and DIPC

_{TIN}) under comparison, for a total of 15 different results (no leaf-on for the 3 cm GSD). To assess separately the two survey scenarios considered (survival and establishment), the seedling dataset was split into small (≤30 cm) and regular (>30 cm) seedlings. The split threshold is double the height requirement for the survival survey (15 cm) and half that for the establishment survey (60 cm).

#### 3.1.2. Softcopy Photogrammetry

#### 3.2. Accuracy Assessment

_{i}is the ground-measured height of seedling i, $\widehat{{h}_{i}}$ is its predicted height; n is the number of seedlings covered by the DIPC dataset under assessment; S (n/2) is the value of the middle element in the ordered list S of absolute residuals (i.e., the median absolute error, MEDAE, not to be confused with the mean absolute error, MAE); $\overline{SD}$ is the mean stochastic dominance of the reported result over all other results; m is the total number of results (m = 15); and $S{D}_{jk}$ is the stochastic dominance of result k over result j, which we define as the percentage of n′ seedlings common to j and k where the absolute residual in k is less than that in j. That is, a result with a $\overline{SD}$ value of 67% means that if we randomly pick a seedling and compare its height estimate from this result with that from a randomly selected result, and repeat this experiment many times, the result with $\overline{SD}$ = 67% will yield a more accurate estimate than the other results 67 out of 100 times. MEDAE and SD are robust to outliers and can be tested for significance.

^{2}for the best result at each GSD (so for three results). Since there are several accuracy metrics, what is “best” was determined as the mean combined ranking in those metrics. To avoid the derived trend being affected by outliers, we removed from this analysis seedlings with an absolute residual exceeding twice the RMSE of the corresponding result; such seedlings constituted less than 10% of the seedlings in any of the results. Then we ordered the list of seedlings of each of the three results in ascending order by reference height, selected seedlings 1 to 15 in each list, computed the value of these four metrics on the basis of those 15 seedlings only, and assigned as abscissa their mean reference height, thereby obtaining the first point in the trend graph. Then we repeated the same operation for seedlings 2–17, 4–19, 6–21, and so on until the end of the list was reached. The trend line of the resulting scatterplot was fitted using the Deming R package thielsen function [24], a robust regression method that also provides confidence intervals for the slope and intercept. Finally, to assess the vertical error of the three ground determination methods, RMSE and bias were also computed between the ground elevation estimated by each method and the observed GNSS elevation value for all seedling locations.

## 4. Results

#### 4.1. Height Estimation

#### 4.1.1. DIPC, Seedlings ≤30 cm

^{2}indicate there is no relationship between predicted and observed heights for small seedlings (R

^{2}< 0.1 for all results). Only two out of 15 results have a %RMSE <100 (%RMSE relative to the mean observed height of seedlings in the result): the 0.75 cm leaf-off DTM

_{ALS}(RMSE = 16 cm, %RMSE = 73) and the 0.75 cm leaf-off DIPC

_{TIN}(RMSE = 19 cm; %RMSE = 85), but their R

^{2}is nil (<0.01) (Table S1). A possible explanation for the lack of relationship is that most of the small seedlings are surrounded by other low-lying vegetation that may create points of elevation similar to the apex of the seedling. Since the apex may sometimes not even generate a point, the estimated height hardly depends on the seedling itself. This may be more evident in results that used the DTM

_{ALS}method for ground determination, which include many seedlings for which the estimated height is 0, meaning that the tallest point in the local DIPC had an elevation equal to or lower than the DTM

_{ALS}. For example, over half of the seedlings in the 0.75 cm leaf-on DTM

_{ALS}result have an estimated height of zero, yet this result has an RMSE of 33 cm and an underestimation bias of just 3 cm. This is an indication that RMSE and bias alone are not enough to assess the goodness of a result. An inspection of MEDAE and SD reveals that this particular result has the worst median absolute error (25 cm) and stochastic dominance (19%, meaning that this result performs worse than the other results in four out of five seedlings). Perhaps the clearest sign of the general lack of relationship is the fact that the top-ranking result is different for each of the accuracy metrics, something that could be expected if the results were ranked at random. For an example of the scatter between predicted and observed heights for seedlings ≤30 cm, see the red points in Figure 2, corresponding to the 0.35 cm leaf-off DIPC

_{TIN}.

#### 4.1.2. DIPC, Seedlings >30 cm

_{TIN}, which achieved an RMSE of 24 cm (%RMSE = 40%) and an R

^{2}of 0.63 (Figure 2; Table 3). The worst results came from the 3 cm GSD dataset, where R

^{2}was 0.13 or lower, and RMSE ranged from 67 cm (DTM

_{ALS}ground method) to 75 cm (DIPC

_{TIN}) (Table 3). The 0.35 cm leaf-off DIPC

_{TIN}yielded the best values in all accuracy metrics except for bias and R

^{2}(the best coefficient of determination, R

^{2}= 0.67, was obtained with the exact same DIPC dataset but using the DIPC

_{MIN}method). Wilcoxon unpaired tests indicate that except for the 0.35 cm leaf-on DIPC

_{TIN}, this result yields significantly lower MEDAE than the rest (indeed, it is remarkable that half of the seedlings have an absolute residual of 5 cm or less). On average, the 0.35 cm leaf-off DIPC

_{TIN}outperforms the other results in two-thirds of the seedlings ($\overline{SD}$ = 67%), although only half of the pairwise comparisons are statistically significant.

#### 4.1.3. Softcopy Photogrammetry

#### 4.2. Counting Errors in Seedling Surveys

_{MIN}, which had the largest overestimation bias, 31 cm) to 93% (0.75 cm leaf-off DIPC

_{TIN}, which had the most severe underestimation bias, 17 cm). Since no seedling was shorter than the 15 cm requirement, commission errors could not be assessed for the small seedling set.

_{TIN}) did not result in the lowest counting errors, but the error rates were reasonable (13% omission and no commission). The best compromise would come from the 0.35 cm leaf-on DIPC

_{TIN}(second best in height accuracy), which had an 8% omission rate and a 6% commission rate. Interestingly, there are results at coarser resolutions that would still provide a decent count assuming perfect detection, such as the 0.75 cm leaf-on DIPC

_{MIN}(10% omission rate and 9% commission rate), and the 3 cm leaf-on DTM

_{ALS}(12% omission rate and a 7% commission rate). This suggests that height estimation errors would only have a small impact on seedling counting errors in establishment surveys, probably smaller than detection errors.

## 5. Discussion

#### 5.1. Effect of Ground Sampling Distance (GSD)

_{MIN}ground determination method is probably caused by this noise. Wind may also have played a role. There were gentle wind gusts during some of the acquisitions and moderate turbulence was created by the Mavic Pro when it flew at 5 m AGL to achieve a GSD of 0.35 cm. As Frey et al. [25] explain well, a finer GSD exacerbates wind effects on smaller scene elements that could cause a shift of location in adjacent photos taken even a second apart. Therefore, the finer the GSD, the more influence wind will have. However, given that the best results were nonetheless achieved with the finest GSD, we can assume that, at least for our acquisitions, the detrimental effect of wind did not offset the benefits of a finer GSD. A coarser GSD is less affected by wind, but the flattening effect that can be appreciated in Figure 5 (also in Video S1) leads to a less reliable estimation and a weaker correlation. This finding is consistent with the observation of Frey et al. [25] that a finer GSD and high image overlap are both beneficial for sampling lower parts of the canopy, understory, and ground. In short, in our study, seedling height estimation accuracy and correlation were stronger at finer GSDs; the RMSE at 0.35 cm GSD was less than half that at 3 cm GSD, and their highest R

^{2}values were 0.67 and 0.13, respectively.

#### 5.2. Effect of Leaf Phenology

#### 5.3. Effect of Ground Determination Method

_{TIN}consistently provides smaller absolute residuals than the other ground determination methods. This could be because DIPC

_{TIN}is not affected by below-ground noise from the data, whereas DIPC

_{MIN}is. Although DIPC

_{TIN}yielded the best prediction of seedling height, it does not follow that it provides the best estimate of ground elevation. Comparison of elevation values obtained from each ground determination method with GNSS elevation values revealed that DTM

_{ALS}consistently followed the GNSS-measured elevation better than DIPC

_{TIN}, with a bias of −2 cm and an RMSE of 20 cm for the 69 seedling locations in the 0.35 cm leaf-off dataset, whereas the DIPC

_{TIN}had an RMSE of 25 cm and a bias of −13 cm (for comparison, these figures are 47 cm and −36 cm, respectively, for the DPIC

_{MIN}). Given the poorer height estimation performance using DTM

_{ALS}, it is likely that the point clouds carry local spurious deformations of the true terrain shape that make an ancillary ALS DTM unsuitable for estimation of the height of low vegetation such as seedlings. This is consistent with previous studies, such as Salach et al. [26], who found that the SfM workflow leads to a point cloud that represents terrain elevation with less fidelity than an ALS point cloud. Nevertheless, given that height estimation is relative and given that the top point in the seedling cylinders carries the same local elevation error as the ground points, DIPC

_{TIN}outperforms DTM

_{ALS}. This means that an ancillary ALS DTM is not required, as has been pointed out by the authors of earlier studies [10,27]. The DIPC

_{TIN}method, however, is more sensitive to ground occlusion and snow presence, and the production of a suitable TIN requires some user interaction. The DIPC

_{MIN}method, on the other hand, is simpler, but it is more sensitive to below-ground noise and slope. For coarser GSDs, the ground determination method appears to still make a difference, but the best method is different: DIPC

_{MIN}for 0.75 cm GSD (perhaps because of the absence of below-ground noise in this point cloud), and DTM

_{ALS}for 3 cm GSD (perhaps because of a better representation of the terrain of this point cloud, which had the largest extent and included the highest number of GCPs). Although it requires more user interaction, DIPC

_{TIN}is probably a safer alternative than DIPC

_{MIN}, but more research is needed to confirm this.

#### 5.4. Effect of Seedling Size

^{2}are less reliable given the wide confidence intervals and the absence of a clearly linear pattern, but there seems to be an upward trend at least for the 0.35 cm GSD (Figure 7). These results suggest that DIPC estimates should be more reliable for taller seedlings.

#### 5.5. Errors Contributing to Outliers

^{2}, Figure 4). In particular, we found several sources of outlier-causing errors, some of which could be avoided or reduced in future studies:

- Location error—all seedlings locations were visually checked to determine which of them did not align with their apparent position in the orthomosaics. Seventeen of the 189 seedlings in this study had an offset greater than 20 cm in at least one orthomosaic. There were several instances where the seedling could not be found at their measured location within any of the orthomosaics. However, most of those seedlings were obstructed from view by adjacent trees so we could not assess their location error. Location errors greater than 20 cm are likely to cause an outlier in the height estimation, which only considers DIPC points within a 20 cm radius of the reported locations. Location error is expected through the DIPC workflow, where XYZ coordinates can be shifted from their true geographic location because of complexities within the SfM process [28,29]. This was demonstrated by slight shifts found between orthomosaics of the different DIPC datasets, as well as between the orthomosaics and their input GCPs. Fortunately, in an operational drone survey, seedling locations will come directly from semi-automated seedling detection on the orthomosaic [5], so these locational offsets will be absent.
- Field measurement or data entry error—seedlings that corresponded to obvious outliers in the 0.35 cm GSD leaf-off dataset were checked in relevant field photos or videos. Figure 8a shows an example of such an error where “observed” height is 0.19 cm, but orthomosaics and field photos show this value is probably incorrect. This type of errors inflates the observed RMSE, but we decided to include them because removing outliers is hardly justifiable except for the limited purposes of a sensitivity analysis such as the one we did on seedling size (Section 5.1).
- 3D reconstruction error—for the finest GSD there was below-ground noise (discussed in Section 5.2). Whatever the source of below-ground noise is, it probably also creates spurious points elsewhere in the DIPC, which will affect height estimation if they happen to be local maxima. Additionally, seedlings can be occluded by adjacent taller vegetation, preventing a full reconstruction in the point cloud. As described earlier, wind will also have an impact on 3D reconstruction where the DIPC workflow will have trouble matching the image pixels of swaying objects. Species phenology and morphology also affect 3D reconstruction; bare twigs from deciduous larches will be difficult to fully capture (e.g., Figure 8b). It also seems that jack pine seedlings are harder to reconstruct, perhaps because of their narrow shape. All these effects lead to underestimation bias and are unlikely to be reduced in an operational drone survey, except perhaps by limiting the maximum ambient wind allowed for acquisitions, as suggested by Frey et al. [25].
- Non-seedling point errors—in a naturally regenerating linear disturbance there will be a lot of vegetation present that interferes with height estimation of nearby seedlings. There were several instances where a seedling’s height was overestimated because of neighboring tall shrubs or adjacent mature trees. To reduce this effect, we limited the DIPC extraction to a narrow vertical cylinder design, which is simple, but the inclusion of some points from neighboring vegetation inevitably occurred. A procedure that included point cloud segmentation [30], wherein clusters of points belonging to the same plant are given a unique ID—thus allowing for the removal of neighboring points belonging to an adjacent plant—would solve this problem, although tuning such an algorithm for short vegetation is not trivial.

#### 5.6. Study Contributions and Limitations

#### 5.7. Outlook

^{2}ALS data. The lowest RMSE was 41 cm (−40 cm bias and 11 cm standard deviation) for scots pine in the 0 to 1 m height class (n = 29), which is almost double what we obtained for our best result. Furthermore, the reliability of DIPC height estimates is expected to increase with seedling size. If the trends we found for RMSE could be extrapolated beyond the studied range, a relative RMSE of 10% could be achieved for mean seedling heights greater than 2 m in a scenario where ground points in the point cloud are available and correctly classified, and where interfering points from nearby tall vegetation are removed via segmentation. A GSD of 0.5 cm can be achieved with commercially available cameras mounted on drones flying over the forest canopy. It does not seem feasible using a manned aircraft, however. In addition to the GSD requirement, these aircraft could not easily achieve the large image overlap required for SfM.

## 6. Conclusions

^{2}was 0.13. In contrast, for seedlings >30 cm, these figures greatly improved: they went to 40% (24 cm) and 0.67, respectively.

_{TIN}) had an error of 5 cm or less, and this result outperformed the others in two-thirds of the seedlings. While the best result was leaf-off, it was not significantly better than the second-best result (leaf-on), so it is preferable to plan the acquisitions during the more predictable leaf-on period. Seedling heights estimated with ground elevation based on the DIPC itself were more accurate than heights estimated using an ancillary ALS-based DTM. While RMSE is expected to increase slightly with the mean height of seedlings, it does so at a slow rate, meaning that both %RMSE and R

^{2}are expected to improve with seedling size, at least at the finer GSD.

## Supplementary Materials

^{2}plot with seedlings.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Left: study area location in Alberta, Canada. Center: Close-up of the study area showing the three sites. Upper right: site layout. Middle right: example of drone-based image point cloud (DIPC) orthomosaic of a belt plot in leaf-on conditions. Lower right: Same in leaf-off conditions. NB. The transect line divides the belt plot in two halves, hence there are ten sub-plots, five at each side.

**Figure 2.**Scatterplot of observed (ground-measured) versus predicted heights in the best result for seedlings >30 cm (0.35 cm GSD, leaf-off, DIPC

_{TIN}), including accuracy metrics (in black). The red dots represent seedlings ≤30 cm in this dataset, which were used only for the small-seedling analysis (corresponding accuracy metrics in red). MAE = mean absolute error; MEDAE = median absolute error.

**Figure 3.**Seedling height estimation bias versus root mean square error (RMSE) for all ground sampling distance (GSD), phenology, and ground determination methods. DIPC

_{MIN}= ground elevation set to the minimum of the local DIPC; DTM

_{ALS}= ground elevation based on the light detection and ranging (LiDAR) digital terrain model; DIPC

_{TIN}= ground elevation based on a triangular irregular network derived from the DIPC.

**Figure 4.**Scatterplot of observed (ground-measured) versus predicted heights for seedlings measured both with softcopy (crosses) and drone-based image point clouds (DIPC) (circles), including descriptive stats and accuracy metrics. DIPC

_{TIN}= ground elevation estimated the weighed mean elevation of the three closest nodes in the DIPC triangular irregular network; RMSE = root mean standard error; MAE = mean absolute error; MEDAE = median absolute error.

**Figure 5.**An example illustrating relative point densities, 3D reconstruction detail, and height estimation for a cluster of spruce seedlings (drone and ground photos on the left) using each of the three ground sampling distances (GSD) studied. Points colored according to their height. Note that as GSD coarsens, the corresponding point cloud “flattens” (see also Video S1).

**Figure 6.**A sample vertical profile from the 0.35 cm ground sampling distance (GSD) drone-based image point clouds (DIPCs) (

**a**), and respective leaf-on (

**b**) and leaf-off (

**c**) orthomosaics. The profile was extracted from a 20 cm wide transect (black line with yellow buffer) connecting several surveyed seedlings (white triangles). The height estimates come from the DIPC

_{TIN}method (the weighed mean elevation of the three closest nodes in the DIPC triangular irregular network). The scale of the vertical profile is slightly coarser than that of the displayed images, because the transect is not straight. Ground photos of the 1-m diameter, red and yellow hula-hoop, and a 3D view of the corresponding point clouds from different GSD can be watched in Video S1.

**Figure 7.**Trends in RMSE, magnitude of bias, median absolute error (MEDAE), and R

^{2}as a function of mean seedling height for the best result (0.35 cm GSD, leaf-off, DIPC

_{TIN}). Each point represents a subset of 15 seedlings ordered in ascending order by reference height. Each pair of consecutive points along the x axis shares 13 seedlings. The solid red line is the Theil–Sen regression line, and the dashed lines represent the lower and upper 95% confidence intervals.

**Figure 8.**Example of (

**a**) height overestimation of a spruce seedling (probably due to a data entry blunder) and (

**b**) height underestimation of a larch seedling (leaf-off). The left panels are a nadir view of seedlings from the orthomosaic, the middle is a profile from a field photo, and the right is the 3D reconstruction.

**Table 1.**Drone acquisition parameters and descriptive statistics of ground-measured heights for seedlings used in the analysis of each drone dataset. GSD = ground sampling distance, Sb = black spruce, Pj = jack pine, Lt = larch. NB. The different number of seedlings in the 0.75 cm GSD leaf-on and leaf-off acquisitions, and the different minimum height in the 0.35 cm GSD leaf-on acquisition are due to them having slightly different coverage.

Acquisition Parameters | No. of Seedlings | Seedling Height Statistics (m) | Species | |||||||
---|---|---|---|---|---|---|---|---|---|---|

Phenology | GSD (cm) | Min | Max | Mean | Median | StDev | %Sb | %Pj | %Lt | |

Leaf-on | 0.35 | 69 | 0.16 | 1.59 | 0.49 | 0.37 | 0.34 | 80 | 13 | 7 |

0.75 | 176 | 0.15 | 2.38 | 0.59 | 0.43 | 0.44 | 82 | 6 | 13 | |

3 | 189 | 0.15 | 2.38 | 0.6 | 0.46 | 0.43 | 79 | 5 | 15 | |

Leaf-off | 0.35 | 69 | 0.15 | 1.59 | 0.49 | 0.37 | 0.33 | 78 | 13 | 9 |

0.75 | 189 | 0.15 | 2.38 | 0.6 | 0.46 | 0.43 | 79 | 5 | 15 | |

3 | – |

**Table 2.**Drone acquisition and processing parameters. Mean AGL = mean flight altitude above ground level, SfM GCP err = ground control point positional error from the structure-from-motion workflow, GSD = output ground sampling distance. The density column refers to the output drone-based image point cloud (DIPC) dataset.

Site | Acq. Date | Mean AGL (m) | Flight Conditions | Drone | Camera | Focal Len. (mm) | SfM GCP Err. (cm) | GSD (cm) | Approx. Density (pts/m^{2}) |
---|---|---|---|---|---|---|---|---|---|

460 | 3 August 2017 | 5 | Overcast; variable light winds | DJI Mavic Pro | FC220 | 4.73 | 21.5 | 0.35 | 25,000 |

31.5 | DJI Inspire 2 | FC6510 | 8.8 | 20.9 | 0.75 | 7000 | |||

122 | Variable sun | eBee Sensefly | S.O.D.A | 10.2 | 3 | 3 | 650 | ||

19 October 2017 | 5 | Sunny; gentle wind gusts | DJI Mavic Pro | FC220 | 4.73 | 22.3 | 0.35 | 32,000 | |

31.7 | DJI Inspire 2 | FC6510 | 8.8 | 12.1 | 0.75 | 5000 | |||

464 | 3 August 2017 | 4.7 | Sunny; scattered cloud | DJI Mavic Pro | FC220 | 4.73 | 25.9 | 0.35 | 30,000 |

4 August 2017 | 30.4 | Occasional sun; increasing winds | DJI Inspire 2 | FC6510 | 8.8 | 27.2 | 0.75 | 5000 | |

3 August 2017 | 122 | Variable sun | eBee Sensefly | S.O.D.A | 10.2 | 5.7 | 3 | 940 | |

20 October 2017 | 4.5 | Sunny; gentle wind gusts | DJI Mavic Pro | FC220 | 4.73 | 11.3 | 0.35 | 30,000 | |

30.2 | DJI Inspire 2 | FC6510 | 8.8 | 78 | 0.75 | 4600 | |||

466 | 3 August 2017 | 5 | Occasional sun | DJI Mavic Pro | FC220 | 4.73 | 12.8 | 0.35 | 25,000 |

31 | DJI Inspire 2 | FC6510 | 8.8 | 19 | 0.75 | 4000 | |||

122 | eBee Sensefly | S.O.D.A | 10.2 | 5.6 | 3 | 735 | |||

19 October 2017 | 5 | Sunny; gentle wind gusts | DJI Mavic Pro | FC220 | 4.73 | 8 | 0.35 | 38,000 | |

30.5 | DJI Inspire 2 | FC6510 | 8.8 | 9.2 | 0.75 | 3700 |

**Table 3.**Results for seedlings >30 cm, ordered by the mean value of their ranking in each of the six metrics (e.g., the mean ranking for the 0.35 cm leaf-off DIPC

_{TIN}is (1 + 6 + 1 + 1 + 2 + 1)/6 = 2)). Note that the best value for each metric appears in bold. N is the number of seedlings included in each result, $\overline{h}$ is the mean observed height of those seedlings in m, RMSE is the root mean square error, MAE is the mean absolute error, MEDAE is the median absolute error, R2 is the coefficient of determination, $\overline{\%\mathrm{SD}}$ is the mean stochastic dominance of the result as defined in 3.2, and %om and %com are the percentage of omission and commission error respectively. All metrics given in m, except for R2 which is unitless, and $\overline{\%\mathrm{SD}}$, %om and %com, which are given in percent. An asterisk in the MEDAE column indicates that according to the Wilcoxon test, the MEDAE of that result is significantly greater than the MEDAE of the first result in the table (p < 0.05). An asterisk in the $\overline{\%\mathrm{SD}}$ column indicates that the sign test between that result and the first result was significant (p < 0.05), meaning that that first result yields a significantly larger proportion of seedlings where the absolute residual is less than that of the result with the asterisk.

Rank | GSD (cm) | Phenology | Ground Method | N | $\overline{\mathit{h}}\text{}\left(\mathbf{m}\right)$ | RMSE (m) | BIAS (m) | MAE (m) | MEDAE (m) | R^{2} | $\overline{\mathbf{\%}\mathbf{SD}}$ | %om | %com |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

2.0 | 0.35 | leaf-off | DIPC_{TIN} | 48 | 0.61 | 0.24 | −0.11 | 0.14 | 0.05 | 0.63 | 67 | 13 | 0 |

3.2 | 0.35 | leaf-on | DIPC_{TIN} | 48 | 0.61 | 0.28 | −0.07 | 0.18 | 0.11 | 0.43 | 65 | 8 | 6 |

3.8 | 0.35 | leaf-off | DIPC_{MIN} | 48 | 0.61 | 0.28 | 0.10 | 0.20 | 0.18 * | 0.67 | 57 | 4 | 19 |

5.3 | 0.35 | leaf-on | DTM_{ALS} | 46 | 0.61 | 0.29 | −0.14 | 0.21 | 0.14 * | 0.51 | 52 | 7 | 0 |

5.8 | 0.75 | leaf-on | DIPC_{MIN} | 123 | 0.75 | 0.57 | 0.06 | 0.33 | 0.13 * | 0.26 | 64 | 10 | 9 |

6.8 | 0.35 | leaf-on | DIPC_{MIN} | 46 | 0.61 | 0.29 | 0.15 | 0.24 | 0.22 * | 0.52 | 47 * | 4 | 28 |

7.3 | 0.35 | leaf-off | DTM_{ALS} | 48 | 0.61 | 0.32 | −0.22 | 0.24 | 0.20 * | 0.59 | 44 * | 15 | 0 |

7.3 | 3.00 | leaf-on | DTM_{ALS} | 135 | 0.75 | 0.67 | 0.06 | 0.39 | 0.18 * | 0.13 | 61 | 12 | 7 |

8.8 | 0.75 | leaf-on | DIPC_{TIN} | 123 | 0.75 | 0.47 | −0.19 | 0.34 | 0.24 * | 0.37 | 39 * | 22 | 5 |

9.8 | 0.75 | leaf-off | DTM_{ALS} | 135 | 0.75 | 0.57 | −0.25 | 0.38 | 0.19 * | 0.07 | 58 | 30 | 2 |

10.3 | 3.00 | leaf-on | DIPC_{MIN} | 135 | 0.75 | 0.68 | −0.04 | 0.45 | 0.28 * | 0.10 | 45 * | 19 | 7 |

10.5 | 0.75 | leaf-off | DIPC_{MIN} | 135 | 0.75 | 0.57 | −0.28 | 0.40 | 0.27 * | 0.12 | 54 | 33 | 1 |

10.8 | 0.75 | leaf-on | DTM_{ALS} | 123 | 0.75 | 0.54 | −0.20 | 0.41 | 0.34 * | 0.22 | 35 * | 20 | 16 |

13.8 | 0.75 | leaf-off | DIPC_{TIN} | 135 | 0.75 | 0.67 | −0.45 | 0.54 | 0.39 * | 0.10 | 22 * | 40 | 0 |

14.2 | 3.00 | leaf-on | DIPC_{TIN} | 135 | 0.75 | 0.75 | −0.22 | 0.57 | 0.41 * | 0.09 | 23 * | 33 | 6 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Castilla, G.; Filiatrault, M.; McDermid, G.J.; Gartrell, M. Estimating Individual Conifer Seedling Height Using Drone-Based Image Point Clouds. *Forests* **2020**, *11*, 924.
https://doi.org/10.3390/f11090924

**AMA Style**

Castilla G, Filiatrault M, McDermid GJ, Gartrell M. Estimating Individual Conifer Seedling Height Using Drone-Based Image Point Clouds. *Forests*. 2020; 11(9):924.
https://doi.org/10.3390/f11090924

**Chicago/Turabian Style**

Castilla, Guillermo, Michelle Filiatrault, Gregory J. McDermid, and Michael Gartrell. 2020. "Estimating Individual Conifer Seedling Height Using Drone-Based Image Point Clouds" *Forests* 11, no. 9: 924.
https://doi.org/10.3390/f11090924