## 3 Results and Validation of Tree Height Estimation  
A total of 612 trees were investigated within Area 1 by performing two different tests: Test 1a, which considers the length of the shadow of a specific point on the tree canopy, and Test 1b, which evaluates the maximum length of the shadow to extract the maximum elevation of the canopy (Figure 12). Figure 11: Impact of terrain slope on shadow patterns. Figure 10: Geometric entities used for the tree height, as defined via Equation (1). Test 1a was the most time-consuming due to the difficulty in recognizing the specific corresponding points; two different \"IDs\" were assigned to the segment, \"1\" for the clearly identifiable shadow points (80.72% of the total trees) and \"0\" for points where the shadow was not clearly identifiable (19.28% of the total trees), in order to assess their respective contributions to the results during the subsequent validation process. Test 1b was quicker and more approximate; in fact, it was conducted without identifying specific points on the canopy, but it allowed for the estimation of tree height values, which were useful for conducting faster analyses related to vegetative growth and conditions. Rather than assessing the height of a particular point on the canopy, the maximum height of an individual tree is likely a more meaningful parameter for subsequent vegetative analyses, such as estimating biomass, monitoring canopy development, or assessing growth trends. For the additional forty trees investigated with a more detailed UAV survey, Tests 2 and 3 were conducted to determine the tree height at a specific point of the canopy (along with Test 1a). Specifically, for Test 2, twenty trees were considered in Area 2 (flat area), while for Test 3, twenty trees were studied in Area 3 (steep terrain slope) to consider the effect of the terrain's slope for the calculated tree heights. Increasing the sample size for Tests 2 and 3 could certainly further enhance the reliability of the results, but due to logistical constraints, the available data were restricted to these specific regions. A comparison was made by calculating the difference between the tree heights obtained using Equation (1) and those measured from the UAV point cloud, considering the vertical distance from points on the canopy to those on the DEM. The statistical parameters obtained are shown in Table 2. Therefore, a \(t\)-test to compare the means of the differences obtained from the different methods was performed. In particular, the null hypothesis that the difference between the means tree height obtained from the different methods (Equation (1) vs. Test 1a, Test 1b, Test 2, and Test 3 obtained from UAV measurements) is zero with a significant level of 5% was verified. The graphs in Figure 13 compare the heights calculated using Equation (1) (\(x\)-axis) with those measured via UAV surveys (\(y\)-axis) for Test 1a and Test 1b. In both cases, there is a good agreement between the datasets, as indicated by the points being well distributed around the 1:1 line, which represents the ideal correspondence between calculated and measured values. The regression lines further confirm this agreement, with coefficients of determination (R\({}^{2}\)) of 0.85 and 0.77 for Test 1a and Test 1b, respectively. These values suggest a strong correlation, supporting the reliability of Equation (1) in estimating heights with good accuracy when compared to UAV-derived measurements. The results obtained for Tests 2 and 3 are provided in Appendix A (Figure A1). Figure 12: Different shadow lengths for Test 1a and Test 1b. The frequency distributions of elevation differences between the heights calculated using Equation (1) and those measured via UAV surveys are shown in Figure 14. It can be observed that, for most of the examined plants, the maximum difference between the two heights is on the order of 30, with the mean value on the order of centimeters. The results obtained for Test 2 and Test 3 are provided in Appendix A (Figure A2).