The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
643 
Noises in endpoints of image segments (pixel) 
Camera Pose 
0 
5 
10 
15 
CO{o) 
V 
50.346 
48.183 
40.773 
30.269 
M 
50.346 
50.185 
50.675 
49.630 
y/{o) 
V 
3.582 
4.327 
8.317 
13.104 
M 
3.582 
3.858 
4.303 
1.336 
*>) 
V 
2.787 
0.782 
24.080 
32.333 
M 
2.787 
2.281 
2.074 
6.885 
Xo(m) 
V 
-500.672 
-485.999 
-557.189 
-580.263 
M 
-500.672 
-508.195 
-488.357 
-527.336 
Y 0 (m) 
V 
100.317 
135.713 
-14.467 
-121.659 
M 
100.317 
97.641 
95.361 
92.791 
Z 0 (m) 
V 
650.783 
643.552 
453.882 
451.424 
M 
650.783 
673.415 
658.684 
601.905 
Building 1 
W(m) 
V 
20.000 
22.023 
16.302 
14.941 
M 
20.000 
20.672 
20.147 
18.995 
H(m) 
V 
30.000 
31.710 
21.055 
21.847 
M 
30.000 
30.829 
32.836 
28.907 
Building 2 
a(°) 
V 
30.856 
47.744 
68.578 
66.743 
M 
30.856 
31.214 
31.011 
29.335 
X 3 (m) 
V 
100.512 
293.388 
496.548 
182.584 
M 
100.512 
101.313 
98.044 
100.513 
Y 3 (m) 
V 
-200.217 
-297.293 
-128.671 
-111.903 
M 
-200.217 
-201.372 
-195.254 
-191.698 
L(m) 
V 
26.413 
33.982 
54.871 
29.901 
M 
26.413 
26.433 
25.961 
25.260 
W(m) 
V 
20.927 
46.757 
64.184 
21.700 
M 
20.927 
21.059 
20.650 
20.089 
H(m) 
V 
22.315 
24.475 
27.667 
15.535 
M 
22.315 
22.4.7 
21.821 
20.245 
Table 3. Comparison of the vanishing points based method with 
the model based method using the same noises in endpoints 
Errors from image centre offsets 
The influence of the incorrect image centre on both methods 
was analyzed introducing an error of 5, 10, 15 pixels on x andy 
coordinates of the image centre. In Table 4, entries in column 
with 0 pixel offsets correspond to the experiments with correct 
image centre. The experimental results show that both methods 
are insensitive to errors in the image centre offsets, which 
validate the feasibility of the approximation that the principle 
points lay at the image centre. However, without considering 
the noise in the endpoints of image segments, the accuracy of 
the vanishing points based method is slightly better than model 
based one with the same amount of image centre errors. This 
can be partially explained by the fact that the rotation and 
translation constraints are weak constraints when used 
separately. Small errors in the rotation are amplified into large 
errors in the translation, and subsequently affect the resulted 
building parameters. 
3.2 Real Data Experiments 
We take pictures using a Canon PowerShot SD750 digital 
camera. Figure 2a (3072X2304 pixels) is two boxes, and Figure 
2b (3072X2304 pixels) is the Burnside Hall at the downtown 
campus of McGill University, Montreal. The measured image 
edge features are those black lines digitized using mouse. Table 
5 shows that accuracy of 3D reconstruction from Figure2a using 
the model-based method is much higher than those from the 
vanishing points based methods, especially in the dimension of 
the height. 
Errors in the image centre (pixel) 
Camera Pose 
0 
5 
10 
15 
CO( o) 
V 
50.346 
50.324 
50.302 
50.280 
M 
50.346 
50.296 
50.247 
50.198 
¥(°) 
V 
3.582 
3.582 
3.582 
3.582 
M 
3.582 
3.538 
3.495 
3.452 
V 
2.787 
2.790 
2.793 
2.795 
M 
2.787 
2.865 
2.942 
3.018 
X 0 (m) 
V 
-500.672 
-500.934 
-501.197 
-501.459 
M 
-500.672 
-501.341 
-502.002 
-502.654 
Y 0 (m) 
V 
100.317 
100.392 
100.468 
100.543 
M 
100.317 
100.404 
100.490 
100.574 
Z 0 (m) 
V 
650.783 
650.579 
650.376 
650.172 
M 
650.783 
649.026 
647.276 
645.532 
Building 1 
W(m) 
V 
20.000 
20.009 
20.018 
20.027 
M 
20.000 
19.989 
19.978 
19.967 
H(m) 
V 
30.000 
29.973 
29.945 
29.918 
M 
30.000 
29.879 
29.759 
29.640 
Building 2 
a{o) 
V 
30.856 
30.821 
30.786 
30.751 
M 
30.856 
30.819 
30.782 
30.745 
X 3 (m) 
V 
100.512 
100.403 
100.294 
100.185 
M 
100.512 
100.529 
100.546 
100.564 
Y 3 (m) 
V 
-200.217 
-200.298 
-200.379 
-200.461 
M 
-200.217 
-200.156 
-200.096 
-200.035 
L(m) 
V 
26.413 
26.422 
26.431 
26.441 
M 
26.413 
26.419 
26.424 
26.430 
W(m) 
V 
20.927 
20.928 
20.929 
20.930 
M 
20.927 
20.921 
20.916 
20.910 
H(m) 
V 
22.315 
22.296 
22.278 
22.258 
M 
22.315 
22.242 
22.171 
22.099 
Table 4. Comparison of the vanishing points based method with 
the model based method using the same image centre errors 
Figure 2. (a) Two boxes with digitized edges superimposed (b) 
Burnside Hall with digitized edges superimposed 
The building in Figure2b is an irregular cube but we use a 
rectilinear building model to approximate it, which induces 
measurement errors, especially in the comers of the building. 
Besides, the occlusions caused by snow make the accurate 
measurement of the building top and bottom difficult. Under all 
of this noise, however, we still achieve reasonable results using 
model based approach. The computed dimensions of Burnside 
Hall are 35.44, 34.92, and 53.33 meters respectively, as 
compared to the model dimensions obtained from DWG file of 
35.44, 32.42, 50.00 meters. While the vanishing points based