235 
6. FINAL REMARKS 
The proposed method is simple and economical, 
although not very accurate, neglecting the 
asymmetric distortion and the distortion variation 
with the focussing distance. It reduces 
significantly the number of the unknown 
parameters of collinearity or DLT equations. It 
enables the distortion correction also for long 
focal lenses cameras, achieving a better accuracy 
in the survey, reducing the amount of the needed 
control points. This work is intended to be the 
first step only for a full camera calibration. The 
strategy will be: a) interior orientation estimate 
with no distortion by a bundle procedure; b) 
estimate of the distortion making use of the 
already computed principal point; c) repeat step 
a) and b) up to the convergence 
Acknowledgements - We thank Geotop, 
Ancona, for having lent the Rollei camera. 
Claudio Lagana, Pesaro, has performed the test 
of Minolta lens. 
REFERENCES 
1. Abdel-Aziz, Y.L. 1973. Lens distortion and 
close range photogrammetry. 
Photogrammetric Engineering, 39, 611- 
616. 
2. Abdel-Aziz, Y.L. and Кагата H.M. 1971 
Direct Linear Transformation from 
comparator coordinates into object space 
coordinates in close-range photogrammetry. 
Proc. ASP/U1 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. 26part 5: 26-29. 
6. Fangi G. 1990. The Direct Linear 
Trasformation with the Camera Station 
Points, ISPRS Arch. Intercommission 
working Group IU/rV, 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. Fraser C.S 1982. Accuracy aspects of 
multiple focal setting self-calibration 
applied to non-metric cameras. Photogrammetria 36, 121- 
132. 
10. Fraser C.S 1982. Film unflatness effects in analytical 
photogrammetry ISPRS Arch. Vol. 24partV/l 156-166 
11. Fraser C.S., and Shortis M R. 1992. Variation of distortion 
within the photographic field. Photogrammetric 
Engineering and Remote Sensing, 58(6): 851-855 
12. Fritz L.W. and Slama C. 1978. Multi-plate, multi-exposure 
camera calibration by the stellar method. 
Photogrammetria, 34 199-223 
13. Fryer,J.G. 1986. Lens distortion for close-range 
photogrammetry ISPRS Arch. Vol. 26part 5: 30-37. 
14. Fryer,J.G. and Brown D.C., 1986. Lens distortion for 
close-range photogrammetry, Photogrammetric 
Engineering andRemore Sensing, 52(1): 51-58 
15. Fryer,J.G. 1989 Camera calibration in non-topographic 
photogrammetry handbook on Non-Topographic 
Photogrammetry, American Society of Photogrammetry 
and Remote Sensing, Falls Church, 59-69. 
16. Hakkarainen J. 1978. Determination of radial and 
tangential distortion of reseau cameras with the Helsinki 
university of technology horizontal goniometer. 
Photogrammetria, 34, 133-145 
17. Kruck E. 1985, Bingo, User’s Manual, Hannover 
18. Livingtone, R.G. et a. 1980- Aerial Cameras -Manual of 
Photogrammetry ASP, 
19. Magill, A. A. 1955. Variation in distortion with 
magnification. Journal of research of the national Bureau 
of Standards, 54(3): 153-142 
20. Malan G. and Rinaudo F. 1993. Calibrazione di immagini 
non metriche: esperiuenze e prospettive Bollettino Sifet, 4: 
81-105 
21. Melen T. and Balchen J.G. Modelling and calibration of 
video cameras ISPRS Arch. VolXXXpart 2/2: 569-577. 
22. Patterson J.B. 1978. Calibration of photogrammetric 
cameras Photogrammetria, 34 69-78 
23. Sheng-Wen S., Yi-Ping H. , Wei-Song L. 1995 - When 
should we consider lens distortion in camera calibration, 
Pattern Recognition, n.3, 447-461 
24. Shortis M.R. , and Robson S., Beyer H.A. 1998 Extended 
Lens Model Calibration of Digital Still Video Cameras, 
ISPRS Arch. VolXKXIIpart 5 159-164. 
25. Tayman W.P. 1978. Analytical multicollimatror camera 
calibration. Photogrammetria 34,179-197 
26. Tayman W.P. and Ziemann 1984. H. Photogrammetric 
camera calibration Photogrammetria Vol.39 (2) 31-53 
27. Wei Guo-Qing, De Ma S., 1994 - Implicit end explicit 
camera calibration: theory and experiments IEEE 
transaction on pattern analysis and machine intelligence, 
vol. 16, n.5, pp. 469-479 
28. Ziemann H. 1978. Visual calibration of reseau cameras. 
Photogrammetria, 34 119-132 
29. Ziemann H. 1986. Thoughts on a standard algorithm for 
camera calibration Arch. Vol. 26 part 5, 85-93. 
30. Ziemann H. and El-Hakim S.F. 1982. On the definition of 
lens distortion reference data with odd polynomials. ISPRS 
Arch. Vol. XXIVpart 1: 123-130.