ISPRS Commission III, Vol.34, Part 3A ,,Photogrammetric Computer Vision", Graz, 2002 
5.2. 3D Polygon Coordinates Refinement 
After finding the corresponding polygons from the previous 
step, the 3D coordinates for each roof polygon is computed, 
however the building topology is not yet reconstructed. We 
implement a geometrically constrained least squares model 
in order to refine the locations of the polygon vertices and to 
reconstruct the building topology. The input observations are 
the image coordinates of the polygon vertices, the unknowns 
are the object space coordinates for the 3D polygons, 
however we have to take into consideration the following 
constraints: 
1-The polygon vertices should be in the same plane. 
2-Symmetric polygons should be constrained to have 
symmetric parameters. 
3-Points that are almost in a horizontal plane are constrained 
to have the same elevation. 
4-Nearby vertices should be grouped into one vertex. 
The aim of the refining step is to convert groups of 
neighboring vertices into one vertex, adjust the elevations of 
horizontal points, and reconstruct the correct relativity 
relation between adjacent facets. 
6. RESULTS 
In the following section the results of extracting the 3D 
building wire-frames are shown. Figure 9 shows a sample of 
17 buildings extracted using the presented algorithm. The 
results show the completeness and accuracy of the 3D roofs 
that can be extracted using this system. 
In order to evaluate the accuracy of the extracted buildings, 
the 3D coordinates of 6 building vertices were extracted 
manually and compared with the automatically extracted 
ones. The RMS error for the vertices in all six buildings is 
0.25m. Table 1 shows the detailed analysis for the evaluated 
6 buildings. Seventy-eight vertices were detected out of 80 in 
the 6 buildings. 
  
  
  
  
  
  
  
Building | (X,Y) RMS | (Z)RMS | Missing Vertices 
BLD 1 0.22 0.12 0 
BLD 2 0.32 0.24 1 
BLD 3 0.22 0.37 1 
BLD 4 0.42 0.24 0 
BLD 5 022 0.25 0: 
BLD 6 0.22 0.27 0 
  
  
  
  
  
  
Table 1. Results for Extracting Six Buildings Roofs, RMS in 
meters 
7. CONCLUSIONS 
The results presented in this paper show the great 
improvement that this algorithm adds to the current building 
extraction techniques. The algorithm succeeds in extracting a 
wide range of urban building. The tested data set includes 
simple buildings with one rectangular roof, gabled roof 
buildings, multi store buildings with large relief, and a 
variety of complex buildings. 
The RMS error is about 0.25m. The false regions that were 
wrongly classified in the Neural Network were automatically 
eliminated since they didn't have any correspondence. The 
overall detection rate for both the Neural Network 
classification and the 3D reconstruction is 97.5%. The 
algorithm succeeded in matching the image polygons 
simultaneously across more than two images, this reduced 
the false alarm matches and increased the result accuracy. 
The method can be implemented using any number of 
images. More work is necessary and will be carried out in the 
future to improve the building delineations even further. 
m 
s] 
  
===) 
Figure 9. The Wire-Frames of a Sample of the Extracted 
Buildings