216 
table 3. The adjustments have been performed in three 
conditions: - without distortion (case B), - with the distortion 
got from certificate (case C), - with the distortion estimated 
by grid method (case D). The comparison of the a-posteriori 
sigma-naught, having chosen a significance level oc=5% , 
indicates that cases C )and D) give better results in terms of 
accuracy than case A) and that cases C) and D) are 
equivalent. 
Arrangement of the observed points 
front 
Fig.6 - Plan and front view of the observed directions 
Table 3 
Comparison of the inner parameters 
(mm) 
x m 
Y m 
C 
On 
A) certificate 
0.09 
0.14 
40.08 
B) no-distort. 
-0.09 
-0.13 
40.06 
60.039 
C) Rollei dist. 
0.09 
0.02 
40.09 
60.019 
D) estim.dist. 
0.05 
0.03 
40.06 
60.015 
Table 4 
Hypothesis testing 
a=5% 
B)no dist./vs. QRollei dist. 
Ml 
QRollei dist./vs. Estim. Dist. 
Hn 
Photo 2 - and Photo 3 
3. Test on control relaxation 
From the initial 18 control directions, some of them have 
been removed and the self-calibration repeated. The results in 
terms of difference from the certificate interior orientation 
values are reported on fig. 7. The computation has been 
successful even with three direction only, getting differences 
of dy M =0.061 mm, dx M =0.000mm and dc=-0.075 mm. 
Fig.7 - Variation of the interior oroientation parameters 
with the number of control directions 
4. Conclusions 
The strategy for full calibration is then as follows: 
1 . Perform a self-calibration by bundle adjustment with 
control directions; 
2. Estimate a distortion curve estimation by grid method, 
using the principal point co-ordinates derived from the 
previous step; 
3. Repeat the step 1 and 2 till the convergence say the new 
computed parameters are the same as those computed in the 
Step 1 can be carried out as on-line calibration, when using 
non-metric cameras. On the contrary step 2 is performed off 
line, in laboratory. Of course, the variation of the distortion 
with the focussing distance must be neglected. The expected 
accuracy cannot be very high, but still sufficient for many 
tasks where an accuracy of 1/1000 is enough 
The directions are suitable and available control information 
for terrestrial photogrammetry to strengthen survey geometry. 
REFERENCES 
1. Abdel-Aziz, Y.L. 1973. Lens distortion and close range 
photogrammetry. Photogrammetric Engineering, 39, 
611-616. 
2. Abdel-Aziz, Y.L. and Karara H.M. 1971 Direct Linear 
Transformation from comparator coordinates into object 
space coordinates in close-range photogrammetry. Proc. 
ASP/UI Symp. On Close-Range Photogrammetry, 
Urbana, 1-18 
3. Adams L.P. 1981. The use of non-metric cameras in 
short-range photogrammetry. Photogrammetria 36, 51- 
60 
4. Brown D.C. 1966. Decentering distortion of lenses 
Photogrammetric Engineering 32, 444-462 
5. Faig W. And Shih T.Y. 1986. Critical Configuration of 
object space control points for the direct linear 
transformation ISPRS Arch. Vol. 26 part 5: 26-29. 
6. Fangi G. 1990. The Direct Linear Trasformation with 
the Camera Station Points, ISPRS Arch. 
Intercommission working Group III/IV, Tutorial on 
"Mathematical Aspects of Data Analysis", Rodhes, pp. 
275-293 
7. Fangi G. 1997 Note di Fotogrammetria, Clua, Ancona 
8. Fangi G. 1998 The Coplanarity Condition For The 
Orientation In Surveying - ISPRS Arch. WG VI/3 
Meeting “international Co-operation and Technology 
Transfer” Perugia Febbraio 1998 
9. Fangi, G., Nardinocchi, C. 1999 The Grid Method , A 
Simple Procedure For The Determination Of The Lens 
Radial Distortion - ISPRS Archives VI WG III Mariano 
Cunietti Memorial Meeting Parma February 15-19 
10. Fraser C.S 1982. Accuracy aspects of multiple focal 
setting self-calibration applied to non-metric cameras. 
Photogrammetria 36, 121-132.