265 
Table 3: Relative position errors of backprojected 
control points in reference system S c . 
rad + dec 
rad-r ihm 
rad2 + dec t- thin 
mean Xc 
1/15569 
i/15547 
1:11759 
mean Y c 
1/13202 
1/13172 
1/9403 
std Xc 
L22D32 
1/21990 
1/12542 
std Y c 
i/18518 
1/18555 
1/11295 
As pointed out in tables 2 and 3, beside of performing a 
calibration with less or more distortion parameters, one 
should choose the camera mode! according to lower 
backprojection errors, which are represented by (mean 
Xw, meanY w ) and (std X w , std Y w ) or, equivalently, by 
corresponding relative values computed in I c . while 
(stdr, stdc) can give a feeling of superimposed noise. 
CONCLUSIONS 
Today, the camera calibration is becoming even more 
an important issue in the digital photogrammetry field, 
in the same time non-metric photocameras are widely 
spreading on the market, due their relative low price 
and improvement of image quality, that is sufficient for 
image processing. In order to put in touch these two 
fields, in the ambit of the Photogrammetry course we 
have developed an alternative calibration method, in 
which the Tsai-Lenz and Cohen-Hemiou algorithms 
were properly revised. The procedure was then imple 
mented as teaching software, in which a graphic inter 
face helps the user for data input, evaluation of calibra 
tion parameters results and assessement of Its accuracy. 
The proposed algorithm is able to taken into account 
various combinations of lens distortions, allowing the 
user to choose the best distortion model according to 
the application field and calibration requirements. 
Fig. 5 : DATA window for calibration parameters input 
ACKNOWLEDGEMENTS 
This work was developed with the project “Digital 
surface modeling by laser scanning and GPS for 3D 
city models and digital orthophotos”. partly financed 
by MURST (Italian Ministry- of University and 
Research) in 1998 as a project of relevant national 
interest. National coordinator: Riccardo Galetto, Head 
of the research unit Antonio Vettore. 
REFERENCES 
[1] Canny JL, January' 1990. “A computational appro 
ach to edge detection”. IEEE Transaction on FAME 
vol 8, n° 6, pp 679-698. 
[2] Faig W., December 1975. “Calibration of close- 
range photogrammetric systems: Mathematical for 
mulation”, Photogramme trie Eng. Remote Sensing, 
vol 41, n° 12, pp 1479-1486. 
[3] Tsai R.. August 1987. "A versatile camera cali 
bration technique for high-accuracy 3D machine 
vision metrology using off-the-self tv cameras and 
lenses”, IEEE Journal of Robotics and 
Automation, vol RA-3, n° 4. pp 323-344. 
[4] Press H. W., Teukolsky S. A., Vetterling W. T.. 
Flannery B. P.. S. A., January 1993. “Numerical 
Recipes in C: The Art of Scientific Computing”, 
Cambridge University Press, 2 nd ed., pp 681-685. 
[5] Weng J., Cohen P., Hemiou M., October 1992. 
“Camera calibration with distortion models and 
accuracy evaluation”, IEEE Transaction on PA ML 
vol 14, n° 10, pp965-980. 
Fig. 6 : The PARAMETERS window showing the 
calibration results.