## 4 Results and Analysis
### The Beijing Urban Scene  
A set of experiments in Beijing demonstrate building detection and height-classification using shadow information at the pixel level. The building detection results and subsequent analysis are visualized in Figure 10. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & **Target** & **Precision** & **Recall** & **Omission** & **False Alarm** & **WH 1** \\ \hline \multirow{3}{*}{Random Forest(Sampling ratio 35\%)} & buildings & 72.5\% & 73.4\% & 26.6\% & 27.5\% & - \\ \cline{2-7}  & buildings & & & & & \\  & (road removed) & 78.2\% & 73.4\% & 26.6\% & 21.8\% & - \\ \hline Proposed method & buildings & 98.6\% & 89.8\% & 10.2\% & 1.7\% & 3\% \\ \hline \hline \end{tabular}  
* WH refers to building objects judged at the incorrect height level.  
\end{table} 
Table 3: Accuracy estimation. Figure 9: Steps and results for the building detection and height-classification method: (**a**) shadow detection result; (**b**) vegetation detection result; (**c**) result of seed-block generation; (**d**) building detection and height-classification result; (**e**) binary result of building detection with RF; (**f**) binary result of building detection after road removal. The original image is shown in Figure 1b. The results of the length measurements of the shadows are shown in Figure 10a--red represents the long length; yellow represents the middle length. Figure 10b shows the results of seed-blocks generation. The building detection and height-classification results are shown in Figure 10c, from which we can see that most buildings have been accurately detected and properly classified with different height levels. The shape of the buildings is still a problem, as shown in the boxes of Figure 10d. Considering that a building was detected correctly, regardless of the shape, differences between the ground truth and the results from our method are marked in different colors in Figure 10e, and the errors include omissions marked in pink, false alarms marked in blue, and incorrect height judgments marked in green. Figure 10c,f shows a binary image displaying only building locations. Thus, our building height-classification results can better explain buildings in urban scenes. For the Beijing scene, the buildings are countable in the image. We classified the buildings into three height levels, and counted the number of buildings in each level. There were two cases of incorrect height judgments: when the entire building is recognized at an incorrect height level, it is recorded as WWH, and when part of building is given the incorrect height, it is recorded as PWH. The related Beijing data is shown in Table 4.  
Figure 10: Building detection and classification in the Beijing scene. (**a**) Length measurement of the shadows—red represents the long length; yellow represents the middle length. (**b**) Results of seed-blocks generation. (**c**) Building detection and classification results. (**d**) Building detection results, with errors marked in boxes, blue boxes: parts of buildings’ surroundings were incorrectly regarded as buildings when the surroundings were combined into the same object; the green boxes: parts of buildings in low brightness caused by shadows cannot be recognized. (**e**) Accuracy estimation of building detection, the red box: omissions stem from low-height buildings in shadows (circled in red boxes); the green box: omissions because low-rise buildings are next to trees (circled in green boxes), omissions because of the buildings on the edges of the image. (**f**) Binary results of building detection for the proposed method. In Table 4, it is revealed that the number of buildings in ground truth was 439, the number of correctly detected and classified buildings was 354, and the number of building detected by our method was 386. Irrespective of the height, the precision of our method exceeded 98% in building detection. When considering the height of a building, the precision dropped to 91.6%.