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35
In Fig. 6 we have a co-ordinate system with origin at the center point defined
above. The principal point has the co-ordinates x r y r in this system. They are
assumed to be small in relation to other image co-ordinates. With symbols as
shown in Fig. 6 we obtain the radial distortion as
dr' = F(r)
where
r = |/(.x—x r ) 2 + (y—y r ) 2
The distance between the center and principal points is
r o = ]¡Xr 2 + y r 2
and the radial distortion of the center point is dr o. The rotation /? in the #—y-
plane is assumed positive in a clockwise direction. The polar co-ordinates of
the principal point are /?<>, r\. From similar triangles in Fig. 6 we obtain
dt r o sin (/9—ftp)
dr' r
7.2.1
Fig. 6.
Assymetric radial distor
tion and so called tangen
tial distortion can be cau
sed by an eccentricity of a
central target in relation
to the principal point. See
text.