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
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7. Fangi G. 1997 Note di Fotogrammetria, Clua, Ancona
8. Fangi G. 1998 The Coplanarity Condition For The
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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
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