214 
CONTROL DIRECTIONS FOR THE CALIBRATION OF TERRESTRIAL NON-METRIC CAMERAS 
ISPRS - COMMISSION VI, WG 3 
Gabriele Fangi - Ancona University - Italy - fangi@popcsi.uman.it 
Key words: non-metric cameras, close-range photogrammetry, distortion, calibration 
Abstract: 
The camera calibration methods are essentially distinguished in calibration in the laboratory by optical goniometers and calibration 
in the field by bundle adjustment. In a previous work (Fangi, Nardinocchi, 9, 1999), we set up the so-called grid method for the 
determination of the camera radial distortion curve. The distortion is obtained as the non-linear part of the homographic 
transformation from object plane the image plane. The homographic transformation is a special case of the Direct Linear 
Transformation, where the object space is reduced to an object plane. The principal point is estimated by intersection of the vectors 
of the transformation residuals. Since the determination is separated from full interior orientation calibration, the estimate is not 
very accurate. When the lens is distortion free no principal point can be estimated. The reason for separate the computation of the 
distortion from the interior orientation is that sometimes, especially with narrow angle lens, numerical problems arise, leading to the 
instability of the system solution. Therefore a simple method for full calibration, making use of what we called control directions, has 
been set-up. First the control direction is defined as known direction toward an unknown point, measured directly by means of a 
theodolite whose centre coincides with the exterior nodal point of the camera to be calibrated. In the collinearity equations the 
exterior orientation parameters reduce to three. The grid method is then coupled to the control directions method, in the sense that a 
first estimate of the principal point position can be achieved by this last method, followed by the distortion determination, and finally 
again by bundle adjustment. Some tests are described and shown. 
Introduction 
The camera calibration methods are essentially distinguished 
in calibration in the laboratory by optical goniometers 
(Hakkarainen, 1978, Taymann, 1978) and calibration in the 
field by bundle adjustment (Tayman, 1978, Tayman 
Ziemann, 1984, Ziemann, 1986). Normally for non-metric 
cameras the determination of the radial and tangential 
distortion is carried out contemporary to the interior 
orientation (Abdel-Aziz, 1973, Adams, 1981, Fryer, 1989, 
Kruck, 1985). The distortion varies not only with the 
focussing distance (Fraser, 1982), but also in the depth of 
field (Fryer, 1986, Magill 1955). The configuration of the 
control points can be near to the critical one ( Faig , Shih, 
1986) and the estimation of the interior orientation brings to 
the instability of the system solution. This holds especially 
with marrow angle lenses. A possible solution is to use the 
known terrain co-ordinates of the projection centre as control 
information (Fangi, 1990). Nevertheless the contemporary 
estimation of the distortion and of the interior orientation 
parameters gives high numerical problems. The separation in 
two steps of the calibration procedure can cope with these 
numerical problems. The determination of the radial 
distortion by the grid method (Fangi, Nardinocchi, 1999) 
neglects the possible variations of the distortion. Now here 
the calibration by control direction is proposed as second step 
of the full camera calibration. 
1. The control directions 
In the collinearity equations 
x = x .r 1 (X-X 0 ) + r 4 (y-y 0 ) + r 7 (Z-Z 0 ) 
M /3(X-X 0 ) + r 6 (y-y 0 ) + r 9 (Z-Z 0 ) 
,r 2 (X-X 0 ) + r 6 (y-y 0 ) + /- 8 (Z-Z 0 ) 
r 3(^ - ^o) + r 6 - ^o) + r 9 (Z -Zq) 
the quantities (X-X 0 ), (Y-Y 0 ), (Z-Z 0 ) are 
proportional to the direction cosines of the projective line 
going from the projection centre to the object point. 
This present research has been financed by Cofin97 
cos(A7?) = (X Xq) = sin(0 0 + r) 
d 
COS07?) = (y ~ Yo) = cos(fl 0 + r) (2) 
d 
cos (ZR) = ———- = ctan(0 o + r) 
d 
The directions (horizontal, r and zenital co) can be measured 
with a theodolite whose centre coincides with the projection 
centre O (figure 1). The control direction can be defined as 
the direction toward an unknown point P(X,Y,Z) but visible 
in the image as P’(*,y). 
Fig.l- The measured quantities by theodolite 
The Orientation parameters are for exterior Orientation: a*, 
oty, a*, rotations about the co-ordinate axes and for interior 
Orientation the principal distance c, and the image co 
ordinates x m , y m of the principal point M. In this occasion a* 
= 0 O . is the so-called constant of station or zero bearing. He 
can take full advantage of the terrestrial photogrammetry. 
The operator has the advantage to have more freedom in the 
selection of control directions than in the control points. 
We don’t know exactly were the projection centre is placed. 
The larger the object-camera distance the smaller the 
eccentricity errors; 1/100 mm over 100mm corresponds to 
10cm over 1000 m (figures 2, 3).