Two translations dx 0 and dz 0 of the image coordinates. 
One scale change dc, referred to the principal distance. 
One rotation dx around the camera axis. 
Two rotations dcp and dco around orthogonal axes through the (exterior) 
perspective center. 
The differential formulas relating these regular errors and the corresponding 
errors of the image coordinates are well known, see for instance Haller1 1960 a. 
(1) 
The discrepancies between measured and given image coordinates are defined 
as follows. 
dx x meas X«:. 
(3) 
(4) 
meas 
given 
dz = z. 
meas 
given 
The expressions (1) and (2) are written as errors of the image coordinates, 
caused by differential regular errors of the measurements in the comparator 
(dx 0 , dz 0 , dx), of the principal distance c of the camera, and of the two orienta 
tion angles (p and co of the photograph. Though either errors or correc 
tions may be used in the basic differential formulas, we will here determine 
the corrections of the six preliminary data. Therefore the signs of the right 
side of the expressions (1) and (2) are changed. Furthermore, since redundant 
measurements are assumed to be available, residual corrections v x and v z are 
assumed to be added to the measured coordinates x and z. Hence the residual 
correction equations are obtained in the usual manner: 
(6) 
Note that dx and dz still are defined according to (3) and (4). 
For the adjustment of the discrepancies, normal equations are formed in 
the usual way and solved. The corrections of the preliminary values of the 
six parameters, the standard error of unit weight and the weight- and correla 
tion numbers for the determination of the error propagation from the standard 
error of unit weight are obtained from the solution. Finally, corrections can 
be computed to the measured image coordinates in arbitrary points according