## 4 Results and Discussion
### Height Estimation of Single Objects
#### 4.4.1 Vehicles  
By a visual inspection of the reconstructed Pleiades-based 3D point cloud, it was observable that points corresponding to small vehicles (vehicles with lengths smaller than 5 m) were not elevated against their surroundings. Larger vehicles were reconstructed in height, but not entirely (Figure 4).  
Specifically, Figure 4 represents a truck with a length of \(\sim\)10 m and a real height of 3.5 m that is visible in both Pleiades (a) and WorldView-3 images (b). On the left-hand side are the magnified satellite image details of the vehicle and on the right-hand side are the corresponding reconstructed height color-coded DSM. From the DSMs and the cross profiles (c), it is clearly visible that in contrast to Pleiades, where there is only \(\sim\)1 m elevation change, the WV3-based profile reconstructs the vehicle height up to 2.9 m, which represents \(\sim\)83% of the real height.  
Using Equation (4), the height percentages of 50 measured vehicles were computed for both cases: Pleiades and WorldView-3 sensors. As mentioned in Section 3.2, vehicles were classified into four different groups depending on their lengths, starting with small family cars, of approximately 5 m, followed by vans, trucks, and finally by large articulated lorries with more than 10 m length. For each group, containing between 10 and 13 vehicles, the mean value of the reconstruction height percentage and the standard deviation were determined. They are shown in Figure 5a for both Pleiades (blue) and WorldView-3 (yellow) data. By increasing length, the height percentage also increases, reaching up to 60% (Pleiades) and 92% (WorldView-3). In the case of the Pleiades imagery, small vehicles (\(<\)7 pixels length in image) do not show any height information, while for family cars, vans, and trucks the reconstruction height percentage is less than 30%. It exceeds 50% only for large vehicles (lengths \(>\)10 m, 14 pixels in the image). On the other hand, in WorldView-3 DSMs, vehicles have a good height reconstruction (reaching over 90% for lengths \(>\)10 m, 33 pixels in image). An exception are family cars (\(\sim\)16 pixels length), which have a percentage of less than 40%. The standard deviations of the estimated heights are notably smaller than the overall trend and they become smaller with increasing vehicle length.  
A similar analysis was conducted by using vehicle width as the main parameter for vehicle grouping (Figure 5b). Because small family cars and vans have similar widths (\(\sim\)2 m), they form a single class, followed by trucks (2 to 2.5 m widths), and articulated lorries (2.5 to 3 m widths). Based on the WorldView-3 DSMs, vehicles with up to 2 m widths have \(\sim\)41% of their real height reconstructed. This value is higher when compared with the percentage of the first length-class (37%) because it contains both family cars and vans, leading to an increased mean height percentage and standard deviation. The mean height percentages reach 59% (Pleiades) and 92% (WorldView-3) for the very large  
Figure 4: Height estimation for a truck. (**a**) Pleiades satellite image detail with profile location (left) and reconstructed DSM Z color-coded (right); (**b**) WorldView-3 satellite image detail with profile location (left) and reconstructed DSM Z color-coded (right); (**c**) Pleiades-; and (**d**) WV3-based vehicle profiles of 0.5 m width each from the matched point cloud; the red horizontal line is the corresponding measured reference height.  
vehicles. The increased values of standard deviations suggest a higher variation of the reconstruction height percentages within the width-classes considered. Therefore, the length parameter is more suitable for the description of the vehicle's height estimation.