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2.2 Image data acquisition
For this experiment, we used Two Basler A302fs CCD
cameras. The cameras were operated on a fast serial bus
specified in IEEE 1394, allowing for fast transmission of digital
signals from video cameras directly into the PC.
A CCD camera can be understood as a metric camera because
of its solid CCD matrix. It is assumed that the lens is stably
interconnected with the camera body and the focal length is
fixed. (Suthau, 2000). The technical data of the camera are
listed in Table 1.
Sensor Type Sony ICX075AL/AK - 1/2 inch, HAD,
interline transfer, progressive scan CCD
Pixels 782 (H) x 582 (V)
Pixel Size 8.3 (H) um x 8.3 (V) um
Video Output | 8 bits per pixel, IEEE 1394 Compliant
Lens focal length 16 mm
Table 1: Technical data of the camera
2.3 Calibration
Calibration and orientation of cameras and images are proce-
dures of fundamental importance, in particular for all applica-
tions which rely on the extraction of precise 3-D geometric in-
formation from imagery where a calibration step is as
prerequisite for accurate and reliable results. The calibration
procedure is defined as the determination of geometric devia-
tions of the physical reality from a geometrically ideal imaging
system: the pinhole camera. Often, only the geometric model-
ing of the relation between objects and corresponding image
features is considered, but a complete calibration procedure in-
cludes a more global analysis of lens system, sensor, and cam-
era electronics
The fundamental mathematical model is the collinearity condi-
tion. It simply express that a point in object space, its corre-
sponding points in the image plane and the centre of perspec-
tive lie on a straight line. Tbe collinearity condition is
expressed by:
XX X-X
p 0 (1)
yc =i DIY -Y, ^
0-c Z-— Ze
where X, y = image coordinates of point
c = camera constant
Xp, ¥p = image coordinates of principal point
Xo, Yo, Zo = coordinates of projection center
X^, Y’, Z’ = object coordinates of point
coordinate system
À =scale factor between image and object vector
D =orthogonal rotation matrix
The deviations of the physical reality from the ideal imaging
geometry of the collinearity condition lead to systematic errors.
These errors are compensated with correction terms for the im-
age coordinates that are functions of a set of additional parame-
ters. À set of these parameters consists of the parameters of in-
terior orientation (Ax, Ay, Ac), a scale factor for the
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004
uncertainty in pixel spacing (S,), a shear factor (A) modelling a
non-orthogonality of the image coordinate system, the parame-
ters: describing symmetrical radial lens distortion (K,, K», K:)
and parameters of decentring lens distortion (Pl, P2) (Re-
mondio, 2002). The extended collinearity equations have the
following form:
l
Xr XX aE E d = Amy
(2)
Ym Yam 8 + Ay
where
AX = AX, ~~ Ac—xS_ + yA +xr’K, +xr'K, + xr°K,
c
(r? 4 2x )P, 2xyP,
y ares - = (3)
Ay= Ay, -—Ac-xA+yr’K,+yr‘K,+yr‘K;
e
12x yP, +(r? +2y )P,
with: x ex-x, ysy-y, Be > ey (4)
A step calibration target plate is employed that provides a three-
dimensional target field, as shown in Figure 3.The calibration
object was taken at a distance of approximately 50 cm and at
the principal distance of 16 mm from the CCD camera from 8
different directions and positions.
Figure 3: Calibration object
The software package PICTRAN which produced by Technet
Gmbh is used. A set of 4 additional parameters was used to
compensate systematic errors. This package enables us to de-
termine calibration parameters for more than one camera simul-
taneously.
The parameters of the interior orientation of the cameras and
the exterior orientation for each camera were determined with a
least squares bundle adjustment. Table 2 lists the estimated
camera calibration parameters and their standard deviations for
one of the two cameras. Similar results were obtained for the
other camera.
In order to test the absolute accuracy of the configuration, we
calculated the coordinates of the calibration points as new
points. The achieved accuracy of the 3D measurement is 0,1
mm in X- and Y-direction and 0,15 mm in Z.
