Orientation Parameters - Transformations
1. Interior Orientation
From the camera calibration protocol of the Leica RC20 the principal point of autocollimation (PPA) is given as (-0.012 mm, -0.005 mm) and the camera's principal distance as 214.74 mm. Radial lens distortion is on the order -2.3 to 4.8 microns. For object reconstruction purposes the given calibration values can be adopted. By ignoring radial distortion and other additional parameters (APs) the camera model required is simplified without significant loss of accuracy. The units of the image coordinates should be
mm for all affine transformations.
xpixel= a1 + a2 ximage + a3 yimage
ypixel= a4 + a5 ximage + a6 yimage
ximage= a1 + a2 xpixel + a3 ypixel
yimage= a4 + a5 xpixel + a6 ypixel
Parameters for image i1.tif (58.tif)
image-to-pixel
| a1 |
8.329527609919551e+03 |
| a2 |
-7.131895000839620e+01 |
| a3 |
-1.036116634861065e-01 |
| a4 |
8.152161292799678e+03 |
| a5 |
-3.924209332739440e-02 |
| a6 |
7.133126806809679e+01 |
pixel-to-image
| a1 |
1.169585609137468e+02 |
| a2 |
-1.402150661116614e-02 |
| a3 |
-2.036692570944883e-05 |
| a4 |
-1.142215949791606e+02 |
| a5 |
-7.713675664492936e-06 |
| a6 |
1.401908550985939e-02 |
Parameters for image i2.tif (59.tif)
image-to-pixel
| a1 |
8.353152746731206e+03 |
| a2 |
-7.132979651782341e+01 |
| a3 |
-1.269540643978518e-01 |
| a4 |
8.173286265284157e+03 |
| a5 |
-5.173753905724950e-02 |
| a6 |
7.133285795793748e+01 |
pixel-to-image
| a1 |
1.173098540248075e+02 |
| a2 |
-1.401936824581864e-02 |
| a3 |
-2.495075398965650e-05 |
| a4 |
-1.144944560973392e+02 |
| a5 |
-1.016831275230263e-05 |
| a6 |
1.401876672957178e-02 |
Parameters for image i3.tif (87.tif)
image-to-pixel
| a1 |
8.378277511392196e+03 |
| a2 |
-7.133905273469587e+01 |
| a3 |
-9.270610876739746e-02 |
| a4 |
8.152536246787537e+03 |
| a5 |
-2.061460558348070e-02 |
| a6 |
7.134228728912908e+01 |
pixel-to-image
| a1 |
1.175915260093767e+02 |
| a2 |
-1.401756220274022e-02 |
| a3 |
-1.821517097916253e-05 |
| a4 |
-1.142395682945267e+02 |
| a5 |
-4.050447714802842e-06 |
| a6 |
1.401692683238062e-02 |
Parameters for image i4.tif (88.tif)
image-to-pixel
| a1 |
8.384152687643529e+03 |
| a2 |
-7.133598652485367e+01 |
| a3 |
-1.191730770556034e-01 |
| a4 |
8.232286234717112e+03 |
| a5 |
-5.167976333985249e-02 |
| a6 |
7.133757280189678e+01 |
pixel-to-image
| a1 |
1.177231200153173e+02 |
| a2 |
-1.401815309518250e-02 |
| a3 |
-2.341804707217700e-05 |
| a4 |
-1.153137391919102e+02 |
| a5 |
-1.015530256864328e-05 |
| a6 |
1.401784140019694e-02 |
2. Exterior Orientation:
In this section the (six) exterior orientation parameters of each of the four images is given in the form of the location of the perspective centers in the Swiss Landeskoordinatensystem in meters and the rotation angles (in grad). They were derived by orientation of single models (58 and 59 pair, 87 and 88 pair) at an analytical plotter using ground control points measured with GPS with an accuracy of ca. 1 dm. The rotation system is omega,phi,kappa.(omega primary, phi secondary),i.e. R = Romega * Rphi * Rkappa. The angles describe the rotation from object to image coordinate system.
Xo, Yo and Zo are in [m]
omega, phi, kappa in [grad]
Image 2087 (i3.tif):
|
Xo
|
Yo
|
Zo
|
omega
|
phi
|
kappa
|
|
679933.474
|
251161.625
|
1521.868
|
0.7991
|
-0.9116
|
162.3969
|
Image 2088 (i4.tif):
|
Xo
|
Yo
|
Zo
|
omega
|
phi
|
kappa
|
|
680240.899
|
250956.277
|
1523.270
|
0.4837
|
-0.9689
|
162.2631
|
Image 2058 (i1.tif):
|
Xo
|
Yo
|
Zo
|
omega
|
phi
|
kappa
|
|
679523.670
|
250761.547
|
1480.194
|
0.3027
|
-0.7627
|
162.1962
|
Image 2059 (i2.tif):
|
Xo
|
Yo
|
Zo
|
omega
|
phi
|
kappa
|
|
679848.592
|
250524.205
|
1479.335
|
0.9050
|
-1.0488
|
162.9081
|
see Rotation matrices in the pdf document of this description
Table 4 Exterior Orientation parameters
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© Institute of Geodesy and Photogrammetry,ETH Zurich