The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part B4. Beijing 2008 
are selected individually in each image. Therefore the number 
of Sj values will be bigger. 
By using the same example (Figure 7) used already in the first 
option a quite unsatisfying result is obtained shown in Figure 8. 
Figure 8. Side view of straight lines extracted by second option 
From the estimated accuracy the low quality could be already 
expected as can be seen in Table 3. 
■—__<\ccuracy(m) 
Line No 
X, 
Y, 
z, 
x 2 
y 2 
z 2 
1 
0.06 
0.10 
0.46 
0.09 
0.21 
0.47 
2 
0.01 
10.63 
0.44 
0.12 
11.46 
0.64 
3 
0.19 
0.29 
3.56 
3.90 
0.96 
1.28 
4 
0.18 
3.56 
0.96 
0.29 
3.9 
1.26 
Table 3. Accuracy of endpoints in each adjusted straight line in 
second approach 
The reason for this low quality was found by investigating the 
geometry of the 3D lines and the 3D projection centers. 
Building edges which are nearly parallel to the base (the 3D 
connecting line of the projection centers) define one plane in 
the three dimensional object space. The consequence is a de 
facto singularity in the adjustment of the 3D line parameters. 
This singularity can be avoided by using images in which line 
through the projection centers is perpendicular to the direction 
of straight lines. So for the lines number 1 and 3, one set of 
images are used and for the lines number 2 and 4, another set of 
images are used. The table below shows the accuracy of the 
endpoints after using appropriate images. 
Amir^rylml 
Line No. 
X, 
Y, 
z, 
x 2 
y 2 
z 2 
1 
0.19 
0.42 
0.98 
0.44 
0.22 
1.24 
2 
0.09 
0.56 
0.3 
0.68 
0.53 
0.29 
3 
0.19 
0.42 
0.98 
0.44 
0.22 
1.24 
4 
0.14 
0.32 
0.5 
0.11 
0.37 
0.46 
Table 4. Accuracy of endpoints in each adjusted straight line 
with appropriate images 
The improvement (compared with Figure 8) can be easily seen 
from the figure below. 
Figure 9. Result found by properly selected image pairs. For 
details see the text. 
The approach in which the lines and the endpoints of the lines 
are automatically selected (option 3) is illustrated in Figures 10 
to 12. The test region shows a part of the New Castle in 
Stuttgart, Germany. One of the extracted edges is shown in 
Figure 10. End points are found by tracking along the edge. 
Figure 10. Straight line extracted by the Hough transform 
In a first view the extracted line looks almost perfect. A closer 
look reveals (Figure 11) that the position of the corresponding 
endpoints in both aerial images differs by several pixels. These 
different positions directly influence the result of the adjustment 
procedure. 
Figure 11. Localised corresponding endpoints in two images 
Figure 12. Adjusted straight line (red line) using the endpoints 
found through the Hough transform and line tracking. 
The blue line shows the position of the straight line based on 
given LIDAR data (initial values). The red line represents 
position of the extracted straight line which is obviously not 
fitting to the building ridge perfectly. 
5. CONCLUSION 
The investigations into 3D line extraction shows that there is 
still a lot of research required if the goal is to extract 3D lines 
reliably and accurate. Best results we have got by measuring the 
endpoints of straight lines manually but this, of course, is not 
really an alternative to traditional photogrammetric point based 
restitution. 
The automated process with Canny edge detection and Hough 
line extraction yields results which are even weaker than the 
results using manual endpoint measurements. Probably the 
model with four line parameters plus one parameter for each 
point on the line is not really suited in combination with 
automated edge feature point extraction. 
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