and the camera constant must be determined. Further-
more, imperfections in the specifications of the sensor
element spacing cause a differentiation in scale along the
two axes of the image.
In order to enhance the geometric quality of the results,
all the above problems should be solved with appropriate
system calibration. The calibration model used in this test
is shown in eqs (1) and described fully in (Beyer, 1992).
X v — "o — à
AX = AX, -—Ac- xsy + ya+ xr Kı tg Kot
C
wg 2: 9 =
+ XI Ks +(r" +2x")P; +2 y P, mn
y +1,23 =
Ay - Ay, -—Ac-0+ xa+ yr, K, + yr^K, *
C
«y r*K, *2x y Pj an £2y P;
where:
Ax, Ay, Ac Change of interior orientation parameters
Sy Scale factor in x direction
a Shear factor (affinity)
K,, K,, K3 First three parameters for radial !ens
distortion
P,P, First two parameters for decentering lens
distortion
X =X-X p
ye yy
r= vx + y?
CAMERA CALIBRATION CHARACTERISTICS
Nominal values
Xp 0.029 mm (384.00 pixels)
Yp - 0.129 mm (287.50 pixels)
C 8.959 mm
Additional Parameters
AXp -4.51 1073 mm
Ayp 5.53 107^ mm
Ac 1.18 107^ mm
S -2.09 1076
a 3.05 1074
K, -1.46 1073
K, 5.78 10°
K3 0
P, -3.56 1074
P, 1.92 104
To obtain precise calibration parameters for the cam-
corder, a testfiled calibration was performed. The 3-D
testfield spans 2.6x2.0x1.1 m? and contains 162 targets.
460
Two images at each of four camera stations were taken,
one image being acquired with the camera in upright
position and the other with the camera rotated 909 around
its optical axis. The above described set of 10 additional
parameters was used for the calibration, in order to
compensate the effects of systematic errors introduced by
the non-ideal geometric characteristics of the imaging
system. The camcorder has been calibrated using the
above described ETH calibration testfield (Beyer, et. al.,
1992) and the values of the additional parameters entering
the above calibration model have been estimated as
shown below with a precision of several micrometers.
5.2 Bundle adjustment
All the measured image coordinates entered the bundle
adjustment for a minimum constrained solution (only 7
parameters for the datum definition are assumed fixed). In
the first set of adjustments, only the object coordinates
are assumed unknown, whereas the systematic errors are
taken care by a pre-calibration using the calibration model
described above together with the obtained values for the
parameters. For the second set of adjustments the
additional parameters for systematic error compensation
are also assumed unkown, using their known values only
as approximate ones. In the latter case the minimum
number of constraints needed for the datum definition are
17 (10 are attributed to the A.P's).
From the 15 known points (their coordinates are known
from surveying measurements) in the first facade, the
minimum number are kept fixed as control points and the
rest serve as check points.
5.3 Transformation to a common frame
In order for the above results to be compatible to the
results obtained by the other participants in this CIPA
test, the minimum constrained solutions obtained so far
should be transfered to the same reference frame with the
rest of the solutions. This reference frame (Patias, et. al.,
1993) is uniquely defined, it provides the minimum norm
and it is obtained by the free-network adjustment.
The transformation of the minimum constrained solution
to a free-network solution requires a Helmert transforma-
tion. The points kept fixed (base points) during this
transformation are the same as those used by the other
participants. The coordinates and the respective variance-
covariance matrix are then transferred to their free-
network respectives.
In order to access the accuracy of the adjusted
coordinates we computed a number of criteria, ranging
from local criteria (characterizing individual points) to
global criteria (characterizing the whole solution). It
should be pointed out that all these are accuracy criteria
since they refer to the actually known (from surveying
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
measure
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