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1.4 Geometric Calibration of Single and Multiple Cameras
Camera calibration aims for a determination of the transformation parameters be-
tween the camera lens and the image plane as well as between the camera and the
scene based on the acquisition of images of a calibration rig with a known spa-
tial structure. This section first outlines early camera calibration approaches as de-
scribed by Clarke and Fryer (
1998
) (cf. Sect.
1.4.1
). It then describes the direct lin-
ear transform (DLT) approach (cf. Sect.
1.4.2
) and the methods by Tsai (
1987
)(cf.
Sect.
1.4.3
) and Zhang (
1999a
) (cf. Sect.
1.4.4
), which are classical techniques for
simultaneous intrinsic and extrinsic camera calibration especially suited for fast and
reliable calibration of standard video cameras and lenses commonly used in com-
puter vision applications, and the camera calibration toolbox by Bouguet (
2007
)
(cf. Sect.
1.4.5
). Furthermore, an overview of self-calibration techniques is given
(cf. Sect.
1.4.6
), and the semi-automatic calibration procedure for multi-camera sys-
tems introduced by Krüger et al. (
2004
) (cf. Sect.
1.4.7
), which is based on a fully
automatic extraction of control points from the calibration images, and the corner
localisation approach by Krüger and Wöhler (
2011
) (cf. Sect.
1.4.8
) are described.
1.4.1 Methods for Intrinsic Camera Calibration
According to the detailed survey by Clarke and Fryer (
1998
), early approaches to
camera calibration in the field of aerial photography in the first half of the twenti-
eth century mainly dealt with the determination of the intrinsic camera parameters,
which was carried out in a laboratory. This was feasible in practise due to the fact
that aerial (metric) camera lenses are focused to infinity in a fixed manner and do
not contain iris elements. The principal distance, in this case being equal to the focal
length, was computed by determining the angular projection properties of the lens,
taking a plate with markers as a reference. An average 'calibrated' value of the prin-
cipal distance was selected based on measurements along several radial lines in the
image plane, best compensating the effects of radial distortion, which was thus only
taken into account in an implicit manner. The position of the principal point was
determined based on an autocollimation method. In stereoplotting devices, radial
distortion was compensated by optical correction elements. Due to the low resolu-
tion of the film used for image acquisition, there was no need to take into account
tangential distortion.
Clarke and Fryer (
1998
) continue with the description of an analytic model of
lens distortion based on a power series expansion which has been introduced by
Brown (
1966
), and which is still utilised in modern calibration approaches (cf. also
(
1.3
) and (
1.4
)). These approaches involve the simultaneous determination of lens
parameters, extrinsic camera orientation, and coordinates of control points in the
scene in the camera coordinate system, based on the bundle adjustment method.
A different method for the determination of radial and tangential distortion param-
eters outlined by Clarke and Fryer (
1998
) is plumb line calibration (Brown,
1971
),
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