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# Full text

Title
International cooperation and technology transfer
Author
Mussio, Luigi

215
Fig. 2 - Off-set of the theodolite
Fig. 3 - Off-set of the theodolite
This case is a special case of self-calibration bundle
adjustmeent proceduce, with one bundle only , the unknowns
being the 3 interior orientation parameters and the the 3
rotation angle.
The control directions can be used by an operator also for any
bundle adjustment: he has to observe with a theodolite the
direction to a far point. The coordinates of this points must
not be computed. These special points can remain unknown,
but they can be used as they were knon points. They can be
observed from one theodolite station only. In case that they
are obrserved from more than one theodolite station, it is
preferable that their co-ordinates remain unknowns becuase
otherwise they can spoil to accuracy of the whole adjustemnt,
due to the maybe poor intersection. The condition to be
satisfied is that the theodolite center coincide with the image
projection center. In addition the angular measurements must
be carried out immediately after of before the photograph, in
order to avoid the possibility of change of the refraction. This
solution is in a certain sense similar to the so-called stellar
method (Fritz , Slama, 1978), apart the differences in term of
means and tools and accuracy, because also in this case one
makes use of known directions towards unknown points, the
stars.
Obviously the solution of (1), expressed in a linearised form,
(4), takes place starting from approximated values for the
unknown parameters. The convergency is fast, and is
achieved also for initial values different even more than 50%
of the final ones. In order to have a null initial value for the
rotation i3 0 , (fig. 1), the origin of the horizontal direction is
set toward the presumed centre of the image. The remaing
two rotations are set to zero.
^x — 0ty—0C Z —0Q—0
«li
«21
¿>21
a l2
a 22
b\2
b 22
«13
«23
b\3
^23
1
dx M
dy M
-
dc
dcc x
da y
da.
o:
(4)
X-XQ
y-y o
The coefficients a*, b*, are the partial derivatives and Xq, y
the values of (1) in correspondence of the approximatec
values of the unknown parameters (Fangi, 7, 1997).
2. The experiments
In order to verify the feasibilty of the proposed method, we
made three tests. The symmetric distribution of the directions
is of great importance.
2.1 - Test n. 1
The first test was carried out selecting a panoramic place to
be photographed (Photo 1). We selected 24 points on the
landscape and by means of a theodolite we measured the
directions towards those points. The camera utilised was a
metric camera Wild P32, practically a distortion-free camera.
The results of the adjustment are shown in table 1. They are
satisfying apart a very large difference for the y of the
principal point, with an error of 0.68 mm. Probably this large
difference could be due to the arrangement of the control
direction very close to one plane spraid in x direction.
Table 1 : Test n. 1 - Metric camera Wild p32
Xlvlimml
^Mitrimi
Certificate
0.00
0.00
63.93
Estimated
0.00
0.68
63.92
- Photo 1
2.2 - Test n. 2
We repeated the experiment with a semi-metric camera
Rollei 6008 equipped with 40 mm focal length lens Distagon.
(Photo 2). The distortion curve (figure 4) was already
estimated by grid method (Fangi, Nardinocchi, 9, 1999).
Rollei camera
The results are reported on table 2.
In this case also a rather large difference in Y for the
principal point is noted (dY M =0.17 mm)
Table 2 - Test n. 2: Semi-metric camera Rollei 6008
(mm)
X M
Y M
c
Certificate
0.09
0.14
40.08
Estimated
0.07
-0.03
40.12
Fig.5 - Plan of the control directions
2. 3 - Test n. 3 semi-metric camera Rollei 6008
To have a better control directions pattern, another place was
selected (photo 3). 18 well distributed control directions have
been selected, (fig.6). The results of the calibration are on