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.

x_pixel= a₁ + a₂ x_image + a₃ y_image

y_pixel= a₄ + a₅ x_image + a₆ y_image

x_image= a₁ + a₂ x_pixel + a₃ y_pixel

y_image= a₄ + a₅ x_pixel + a₆ y_pixel

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

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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.

X_o, Y_o and Z_o 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