3 
in the image xd, Ya 2s well as the partial derivations Lae 
to fg are calculated by using tne transformation parame- 
ters contained in (2.1). 
An AP operates according to the described algorithm as follows: 
The model is subdivided into spatial segments. For each seg- 
nent the centre coordinates Po, the appertaining image co- 
ordinates Pe ‚and. the appertaining values of the partial 
differentials and of the remainder terms are stored. Each 
tine when passing from one segment to a neighbouring segment 
the entire parameter set is changed (Fig. 2.1). 
35 ct «+ 
ti 
3. APPLICATION OF TAYLOR'S FORMULA 70 CEHNTRAL-PERSPECTIVZ 
IMAGES 
3.1 Derivation of the partial differentials 
The fundamental relationships of analytical photozrammetry 
between image coordinates x', y! and model coordinates X4 UJ. 
are for the left image 
N 
-} 
x E X a4 
y! = 1/N . A 4 yy (3.4%) 
-C ge ZA > 
From these follow the two well-known collinearity equations. 
Expanding them according to (2.2) we obtain 
x x! dx n | c 0 se 
x 1 e - 
ai. Fed dy | + with F, = = = wit] 
y' yg dz Ry! e [O3 € uM 
{ = es oth J: aa Da CU m ag (3.2) 
3.2 Derivation and discussion of the remainder terns 
According to the possibilities shown in Section 2. the calcu- 
lation of the remainder  Serms: is first accomplished by 
inversion of (2.2). 
Ro sx'-x»€d4, Rs y! Rye dy (3.5) 
For the renainder terms in matrix notation one obtains 
Red! d dx! 
X 4 
si. ME. (3.6) 
Ry) Cord dy" 
with ad = agy'dkx + azydy + azı-dz. 
The comparison of (3.6) with the remainder terms according 
to (2.3) leads to the relationship 
Taylor (= 0) 
  
B. ne 
" ect Y Th a (3.7) 
Taylor = ( 
Ry $, «4$ Ryr 
- 
Hy 
in an aerial photo pair height differences of + 15% of the 
505 +