## 4 Results and Discussion
### Height Estimation of Single Objects
#### 4.4.3 Buildings  
The third category of objects investigated were single buildings, usually in suburban and rural areas. They usually had regular geometric shapes, such as rectangles or squares, which facilitated the visual identification of the corresponding dimensions in the rectified images. The building length/width were measured in the rectified images, based on their roof top view. For buildings with a T- or L-shaped plan, we considered the length as the longest dimension between extreme roof edges, whereas the width as the distance across the roof from one side to the other. One hundred buildings were chosen to cover a wide range of dimensions from 1 to 50 m length (large industrial buildings) and widths from 1 to 25 m. In the example shown in Figure 8b, the two small buildings are elevated against their surroundings in the WorldView-3 data, which is not the case for the Pleiades data. In addition, the profile (d) with two overlaid point clouds corresponding to a 3.6 by 2.5 m building clearly reveals the higher potential of WorldView-3 sensor for height reconstruction, as opposed to Pleiades. Even if the building edges appear very smooth, the corresponding main height is still reconstructed. Again, Equation (4) was applied for investigating the potential of Pleiades and WorldView-3 DSMs for building's height estimation with respect to their lengths and widths (Figure 9). Based on their length, we defined ten different categories, each containing approximately ten buildings (Figure 9a). Like in the previous analyses for vehicles and trees, the computed mean height percentages for buildings show a similar trend, values gradually increasing with building length. In case of the Pleiades imagery, buildings with lengths smaller than 10 m (14 pixels in image space) have a height  
Figure 8: Height estimation of a deciduous tree and a small building: (**a**) Pleiades (first row) and WorldView-3 (second row) views with corresponding height–color coded DSMs; (**b**) RGB colored 3D point clouds, 1 m width height profiles from the matched point clouds; (**c**) for a deciduous tree; (**d**) for a small building; the red horizontal lines are the corresponding measured reference heights. reconstruction percentage of less than 30%, whereas buildings with lengths greater than 5 m have percentages beyond 50%. For both Pleiades and WorldView-3, buildings with lengths \(>\)43 pixels have over 90% height reconstruction. Due to the lower variation in building-width, we considered only five intervals, starting from 0-5 m to 20-25 m (Figure 9b). Compared with height-percentage analysis based on building length, for the width parameter the situation was different. When buildings were grouped based on their corresponding widths, we had an increased number of items within each interval (only 5 width-intervals). This led to a higher variation of height estimation percentages, and hence to higher values for the standard deviations within each interval. When analyzing the reconstruction height percentages based on the WorldView-3 images for both 0-5 m and 5-10 m length/width intervals, we could see higher mean values for the reconstruction percentages computed based on building widths. Nevertheless, the corresponding standard deviations are larger in contrast to those computed on the length basis. The standard deviations for the length-intervals (Figure 9a) become smaller with increasing building length, showing a clearer trend; therefore, the length parameter gives a better estimation when analyzing the height reconstruction of buildings. The two scatter plots (Figure 10) show the relationships between building length and width and the reconstruction height percentage. As expected, height accuracy is better for WorldView-3 images than for the Pleiades data. The delineation lines separate the buildings with higher and lower reconstruction height percentage (p) than 50%.