irt B3. Istanbul 2004
|, geometry: "Tetra,
The arrows point in
eometry for "Tetra,
stance of 3500 pixel.
at rt).
3x23 em”, assumed
n of these synthetic
oe [Ressl 2003]. The
ed in the following
he different compu-
ne
uration, if the num-
| increases, and
jint, correspondence,
geometry increases.
ls for Tetra’, ’Airl’
nwards for ’Streetl’
ethods return prac-
he simple direct lin-
; Lo the rigorous con-
imizing reprojection
spondences, < 8 for
Airl’ and ’Air2’ and
treet1’ and ’Street2’
nimization of repro-
| better than any al-
ined) minimization.
ing only reprojection
7 only the constraints.
inimum thickness of
tation methods, we
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
0.05
Php
0.045
PCC
0.04 -
kbhh
0.035
0.037
Fhbhhbhbbbl
0.025 |
Mean and Max Ground Error [m]
0.005}
9.97 9..9
u A
25 8.3 2.8 0.9 0.3
Cuboid variation in %
JCA
— UCR
-9- CR |
—— 8
CR*
80H © CA
a
e
T
da
e
T
Percentage of failures
Jn
25 83 2.8 0.9 0.3
Cuboid variation in 95
Figure 2: Plot of the mean and maximum ground errors for the "Tetra? configuration using: 8 points, 1 pixel noise,
camera distance: 3 m, threshold for failures: 0.025 m. The mean ground error is plotted with thin lines, the maximum
ground error with thick lines.
for image configurations with strong geometry,
i.e. "Tetra', ’Airl’ and ’Air2’, the minimum thick-
ness is practically independent on the computa-
tion method of the tensor, and becomes smaller
for larger numbers of point correspondences.
- forimage configurations with weak geometry, i.e.
’Street 1’ and 'Street2', the minimum thickness is
larger for the algebraic methods and smaller for
the reprojection methods, where the consider-
ation of the internal constraints adds a signifi-
cant additional benefit; and for larger numbers
of point correspondences the minimum thickness
also gets smaller generally.
® Depending on the number of point correspondences,
the computation of the trifocal tensor was still suc-
cessful for the minimum thickness of the cuboid given
in table 1; afterwards it failed. Because of the discrete
cuboid compressions the actual minimum thickness is
smaller than the presented values; i.e. if the percent-
age of failures for one compression is zero and for the
next it is non-zero, then the actual minimum thickness
lies somewhere in between.
4 EXPERIMENTAL RESULTS FROM REAL
DATA
The findings of the previous section suggest that the practi-
cally most relevant image configurations 'Airl' and "Tetra,
could be used also for very flat objects, with a minimum
thickness of about 196 of the camera distance, provided
10 point correspondences are available. One such object
could be the facade of a building.
The Institute of Photogrammetry and Remote Sensing in
Vienna created a test field for the calibration of terrestrial
cameras by sticking retro reflecting targets on the facades
of their inner courtyard; [Ballik 1989]. Due to the known
object coordinates of the targets, these facades provide a
suitable object to test the determination of the trifocal
tensor for nearly coplanar object points using real data.
The right part of figure 3 shows one of three images from
one of the facades, which were taken approx. 35 m away -
from the third floor of the opposite part of the building us-
ing a calibrated Canon EOS 1Ds with a 20 mm objective’.
Considering this camera distance the minimum thickness
of about 1% would correspond to approx. 35 cm. Unfor-
tunately the retro reflecting targets on this facade have a
depth range of only 18 cm. Furthermore, the 20 mm ob-
jective used for this test has a significant amount of radial
image distortion, see figure 3 left part, which was not re-
moved in advance from the three images used for this test.
Also the focal length of 20 mm is significantly different
from the focal length of 32 mm, which was used for the
synthetic Tetra’ configuration.
Because of all these differences between the setup for the
synthetic and the real data, the required thickness of the
object points to successfully determine the trifocal tensor
is larger than 1% of the camera distance and using only
points on the facade fails. Therefore one point (#1) on
the roof significantly behind the facade by 3.3 m has to
be used in the test sample to successfully determine the
trifocal tensor for the three images; see figure 3 right part.
On the selected facade 121 points in total are visible in
all three images and are extracted automatically with an
accuracy of approx. 0.4 pixel”.
The task of this experiment using real data is somewhat
changed compared with the synthetic data: (i) compute
the trifocal tensor for the three images using a subset of
l'Phe digital camera Canon EOS 1Ds is equipped with a
CMOS sensor of size 24 x 36 mm? and 4064 x 2704 pixels.
2This accuracy is better than the 1 pixel noise in the syn-
thetic test, but due to the other prevailing differences (distortion
and camera distance), the required thickness is still larger than
1%.
