## 3 Data Processing and Analyses
### Manual Reference Measurements  
After the image orientation was completed, the manual measurement of the 3D points was performed. For each object, the highest point was selected, such as points on a building's ridge, on a car's roof and tree crown centre (approximation of the tree top). For the 3D restitution, we manually measured the points monoscopically in all three oriented images (forward, nadir and backward), in a multi-aerial view mode. The mean-square error of the \(Z\) object coordinate is given by the following formula [32]:  
\[\sigma_{Z}=\sqrt{2}\cdot m_{B}\cdot\sigma_{B}\cdot\frac{Z}{B}, \tag{1}\]  
with \(\sigma_{Z}\) the object elevation accuracy, \(\sigma_{B}\) the accuracy of image measurement (1/3 rd of a pixel), \(Z\) the altitude of the satellite orbit, \(B\) the base and \(m_{B}\) the satellite image-scale number given by the \(Z\)/\(c\) ratio, where \(c\) is the focal length of the optical system. Due to the large heights, we considered the special case of parallelism between object and image plane; hence a single scale number for the whole satellite image was used. Taking into account these parameters, the estimated accuracy of the \(Z\) object coordinates is 1.36 m and 0.31 m for the Pleiades and WorldView-3 images, respectively. These results suggest a minimum object height of 1 m as a reference height that guarantees a reasonable analysis. Since the smallest investigated cars have around 1.5 m height and buildings and single trees usually have more than 2 m height, the estimated elevation accuracy does not significantly influence our investigations. In a final step, the reference object heights are computed by using the measured \(Z\)-coordinates and the elevations extracted from the LiDAR DTM (with 1 m resolution and \(\sigma_{Z}\) of 0.12 m) at each point's position. Assuming that the measured and extracted \(Z\) values have random and uncorrelated errors, according to the law of error propagation, the uncertainty associated with the manual measurements for reference object height computation is determined by the quadrature of input elevation uncertainties. The geometric parameters, i.e., vehicle length/width, tree crown diameter and building length/width, were directly measured on the rectified images in a geographic information system (GIS) environment. Three different classes of objects were separately investigated:  
1. Vehicles are classified into four groups depending on their length: (1) passenger and family car type, smaller than 5 m; (2) vans having lengths between 5 and 7.5 m; (3) trucks with lengths between 7.5 and 10 m; and (4) articulated lorries, trailers and multi-trailers usually having more than 10 m. The lengths, widths and the corresponding elevations at car's roofs of 50 vehicles are investigated. The computed mean reference heights are 1.5, 2.5, 3.7, and 4 m for family cars, vans, trucks, and articulated lorries, respectively. Related to average object height, the associated uncertainty of the manual height measurement varies between 8% for lorries and 22% for family cars for WorldView-3 and between 34% and 68% for Pleiades. 2. Trees are typically classified into two categories: coniferous and deciduous. Coniferous trees are cone-shaped trees, represented mainly by spruce in our case. The second category is the broad-leaved trees with leaves that fall off on a seasonal basis, mostly represented by beech and oak. We needed to perform this classification due to the different acquisition times: one in June (leaf-on conditions) and the other one in April (leaf-off conditions). The diameter and elevations were measured for 100 trees (50 trees for each category: deciduous and coniferous). Depending on crown diameters, they were grouped into seven categories, beginning with trees with a crown smaller than 2.5 m, and ending at large trees with 10 m diameter.