Figure 4. Measurement of endpoints of the building edge of two 
corresponding images 
Figure 5. Measurement of multiple points of the building edge 
in two images 
With each measured point in one image, one unknown and two 
observation equations are added. If n is the number of images 
and m is the number of the points measured in each image, the 
redundancy is r = n m - 4. With two images and two points per 
image the redundancy is zero. 
Slightly more complex is the situation it the straight lines are 
extracted automatically. The corresponding workflow is shown 
in Figure 6. The measurement of the endpoint is this case is a 
tracking process to find the endpoints of the extracted lines. 
Importing aerial images 
Image cropping for selecting interesting features 
Edge detection using canny operator 
Straight line fitting using 
Hough transform 
Measurement of end-points of 
extracted straight-line 
Estimation of parameters 
of straight line 
(least Square adjustment) 
Iterate until the increments of the 
unknowns are small enough 
Figure 6. Flowchart of the third option (automated line 
extraction) 
The developed MATLAB routine uses Canny edge detection 
and straight line fitting with the Hough transform. The 
approximate information given by the interactive line 
measurement in the LIDAR data defines narrow windows in the 
images in which the building edges are extracted and 
approximated by the straight lines. The endpoints of the straight 
line are found by tracking the points along the line. 
The difference of this approach from the other two options is 
the point selection process. The functional model is the same as 
for the first option. 
4. RESULTS 
The test building used in this study is ‘Landtag von Baden- 
Württemberg’, the building near the Schlossplatz of Stuttgart in 
Germany. 
Figure 7. Straight lines of the test building 
Results for the first option (manual measurement of fixed 
endpoints) are summarized in Tables 1 and 2 based on the 
measurement of endpoints in two aerial images only. 
Parameters 
Line No. 
0 (rad) 
<p (rad) 
x 0 (m) 
yo (m) 
S| (m) 
S2(m) 
1 
I 
1.581 
1.14 
-329.62 
-2794.79 
2183.8 
2235.42 
F 
1.568 
1.15 
-301.25 
-2798.62 
2179.16 
2233.06 
2 
I 
1.558 
-0.44 
-269.99 
2290.11 
2756.35 
2808.74 
F 
1.579 
-0.423 
-330.97 
2242.91 
2787.37 
2841.51 
3 
I 
1.555 
-1.979 
-338.18 
2877.06 
-2194 
-2143.01 
F 
1.571 
-1.993 
-304.56 
2846.33 
-2240.44 
-2186.67 
4 
1 
1.570 
2.708 
-306.97 
-2217.38 
-2822.99 
-2770.45 
F 
1.569 
2.72 
-309.09 
-2179.95 
-2851.03 
-2797.2 
Table 1. Comparison of initial (I) parameters and final adjusted 
(F) parameters of straight lines using four images 
-A£curacy(m) 
Line No! '—» 
X, 
Y, 
z, 
x 2 
y 2 
z 2 
1 
0.14 
0.28 
0.89 
0.15 
0.23 
0.89 
2 
0.35 
1.58 
1.45 
0.39 
1.22 
1.45 
3 
0.44 
0.42 
1.65 
0.42 
0.47 
1.65 
4 
0.4 
0.43 
1.57 
0.37 
0.39 
1.57 
Table 2. Accuracy of endpoints in each adjusted straight line 
The average horizontal accuracy is in the order of three to five 
pixels (20 cm pixel size), the height accuracy of 1 to 1.5 meters 
is approximately 50% worse. The low redundancy obviously 
leads to a moderate overall accuracy. 
The second option leads to more observation equations and 
more unknowns, because in this approach the selected points 
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