The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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batch job. Image measurements, approximate EO parameters 
and marker coordinates are exported to ASCII files, which can 
directly be used for bundle adjustment. 
Figure 8. MATLAB tool for automated 3D measurements 
The following table gives an overview of the H3D calibration 
projects using the Vexcel test field: 
Date 
Lens 
Focus 
# 
Images 
# Points 
August 1, 2007 
35mm 
00 
15 
4780 
50mm 
00 
23 
4900 
80mm 
00 
16 
1900 
March 19, 2008 
35mm 
00 
35 
10600 
50mm 
00 
20 
4960 
80mm 
00 
21 
3100 
50mm 
5m 
18 
4500 
80mm 
5m 
23 
3100 
Table 2. Statistics of the 3D marker measurements 
2.4 Determination of calibration parameters 
The camera calibration parameters were determined using the 
in-house developed bundle adjustment software PhoBA 
(Photogrammetric Bundle Adjustment). The following 
commonly used camera calibration parameters (cp. Luhmann et 
al., 2006) can be determined: 
1. Focal length: c 
2. Principal point: x 0 , y 0 
3. Radial distortion: coefficients ko, kj, k 2 , k 3 
4. Tangential distortion: coefficients b b b 2 
5. Affinity and shear: coefficients c h c 2 
In a first run, all of the calibration projects were adjusted using 
the complete set of calibration parameters (except ko, which is 
100% correlated with the focal length c). Gross errors were 
automatically removed by the built-in data snooping feature of 
PhoBA. From the analysis of these preliminary results, we 
could draw the following conclusions: 
1. Parameters b t , b 2 , k 3 and c 2 are not significant and can 
be eliminated from the adjustment. 
2. Parameter ci describing the deviation from a square 
pixel (scale in x) is significant but varies slightly 
within the different projects. Pixel size is a physical 
constant, so we decided to fix this parameter at a 
mean value, resulting in a pixel size of 6.8 x 
6.801pm. 
3. The principal point offset is relatively large, which 
causes problems when the principal point of 
symmetry (PPS) is assumed to be at the image center. 
We therefore set the PPS equal to PPA for all 
calibration projects. 
In a second and final run, all calibration projects were adjusted 
using only the five significant parameters (and parameter Ct 
fixed at a given value). The remaining calibration parameters 
are highly significant and much less correlated than the original 
parameter set. The following tables present focal length and 
principal point parameter values and sigma naught obtained 
from the bundle adjustment: 
June 25, 2007 
Lens 
c [mm] 
x 0 [pm] 
Yo [pm] 
35 mm 
35.663 
± 0.0007 
-50.1 
±0.4 
279.6 
±0.4 
0.9 
50 mm 
50.286 
±0.0011 
-98.7 
± 0.0006 
240.1 
±0.8 
1.2 
80 mm 
82.354 
± 0.0056 
-176.7 
±3.1 
302.3 
±4.6 
2.9 
July 1,2007 
Lens 
c [mm] 
x 0 [pm] 
Yo [pm] 
°o 
35 mm 
35.642 
±.0012 
-88.0 
±0.6 
184.6 
±0.7 
1.5 
50 mm 
50.280 
±0.0020 
-137.1 
±1.1 
140.5 
±1.2 
2.1 
80 mm 
82.272 
± 0.0083 
-198.1 
±5.0 
196.9 
±6.0 
4.2 
March 19, 2008 
Lens 
c [mm] 
x 0 [pm] 
yo [pm] 
Co 
35 mm 
35.668 
±0.0012 
-70.4 
±0.5 
294.9 
±0.3 
0.7 
50 mm 
50.251 
± 0.0008 
-105.8 
±0.3 
233.3 
±0.5 
0.7 
80 mm 
82.292 
± 0.0042 
-203.8 
±2.0 
281.6 
±2.7 
2.0 
Table 3. Calibration parameters obtained from the 2D target 
August 1,2007 
Lens 
c [mm] 
x 0 rpm] 
yo [pm] 
Ö0 
35 mm 
35.652 
± 0.0004 
-72.9 
±0.2 
225.3 
±0.3 
1.3 
50 mm 
50.251 
± 0.0004 
-117.1 
±0.4 
153.5 
±0.5 
1.5 
80 mm 
82.297 
±0.0017 
-174.2 
± 1.3 
270.5 
± 1.6 
1.4 
March 19, 2008 
Lens 
c [mm] 
x 0 [pm] 
yo [pm] 
o 0 
35 mm 
35.651 
± 0.0002 
-38.33 
±0.2 
288.33 
±0.2 
1.0 
50 mm 
50.256 
± 0.0006 
-85.99 
±0.4 
225.85 
±0.4 
1.3 
80 mm 
82.301 
±0.0011 
-132.47 
± 1.1 
314.26 
± 1.0 
1.1 
Table 4. Parameters obtained from the 3D test field