5 
distortion, or relief displacements are evidently harmless for the deter- 
mination of the x, y-coordinates, provided the photographs are exactly 
vertical and that the principal points can be reconstructed. The in- 
fluence upon the coordinates x, y of small errors in the image coordinates 
2’, y and x^", y" and in the base b can be found from the differential 
formulae of (1) and (2). These formulae are 
l «4 dl s 11 Sd / x’ Sd " d x’ Sdu' 
dh A Sdy' — 
z' a 3 
3 cum | Je CM | 
y po (3) 
y y y ' x' | 
dy moy dy Sdn pu dat pup My dy — Sdy" (4) 
Y 
VS 
b' is the base on the image scale 1: S 
1.15. Error propagation formulae 
We shall assume that the errors of the basic measurements of the 
image coordinates are of accidental character. We shall then investigate 
how these errors propagate to the coordinates x and y according to (1) 
and (2). Further, the compensating effect of control points in various 
positions will be investigated. 
It is clear that the accuracy of the image coordinates x”, y" and x",y A 
in the expressions (1) and (2) will not be uniform for all points though 
the photographie quality is equal. This is due to the fact that the image 
coordinates are referred to coordinate axes which also have to be deter- 
mined from image coordinate measurements. As demonstrated by 
HALLERT 1957 b the weight and correlation numbers of the image co- 
ordinates can formally be determined from a coordinate transformation 
with the aid of two translations and one rotation. 
The weight- and correlation numbers of the image coordinates were 
determined as follows (moreover, see (30)—(33) below) 
y ; 
(ee d ous 5 
me c 
Qyy = yy 2 |1 + p 7 (6) 
2 xy y 
Oo. oa — N A 7 
AB y Q, y p? T b ( ) 
  
VE aA pK aS 
  
  
MÀ À——5