nbols. 
ere s' 
ilarity 
tation 
is the 
id the 
given 
rs are 
>ssary 
r the 
: 0 
int x i 
is this 
Legenstein, Dietmar 
of, oy of, y 
L = ln A HZ dx, ur. 
( j^ 23 ) x, jT os, Xy +... 9x dx, (2.2-2) 
n 
The linearisation coefficients can be combined in the tensor A! : 
I 
M a 
Ox, (2.2-3) 
The contradictions w; are given by the difference of the observation /; and the evaluation of the function at the 
approximate values: 
0 . 09 4 0 
w, —l; - f. Xo eda. enel, | (2.2-4) 
The linearised equation can now be written as: 
J = 
A, dx; =W, (2.2-5) 
Every row of the system of equations (2.2-5) describes a differential geometric locus. In chapter 2.3 these loci are 
discussed in detail. 
The condition of equations (2.1-1, 2.1-2) is special cases of equation (2.1-3), and therefore the linearisation coefficients 
of the general equation are calculated. The coefficients for the other equations can then be derived easily. In the next 
step the differentials for the unknown point X on the contour and for the surface-parameters a; will be calculated. 
Differentials for the point X on contour with coordinates x;: Equation (2.1-3) has to be differentiated with respect to 
x,. Due to the fact that the vector s can be written directly as the difference of the unknown point X on the contour and 
the centre of projection X, in the reference system, the transformation of the image system to the reference system is not 
necessary. 
um 22-6 
S; =X; — Xo, ( ) 
Unfortunately the vector n cannot be written as a function of X right away. Therefore the transformation cannot be 
avoided in this case. Equations (2.1-7) and (2.1-5) have to be combined. 
The differentiation of (2.1-3) with the product- and chain-rule leads to: 
  
JE, _ OE, ON; Ou OmXn 9E 05, (2.2-7) 
dx, On, Out; Ou X, OX ds, OX, 
on 
J__ can be derived from (2.1-5) leading to: 
M 
  
The differential 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B5. Amsterdam 2000. 475