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