The table below shows the relationship between the general approach of 
multiquadric interpolation as described in chapter 2.2 and the geometric case. 
General_case X4-Coordinate Y4-Coordinate 
1 1 
P5 65,5224) Pr Corer Yor Et Py ajo YaoY gd 
2s 2 2 2" aT ue 
se) Sk" (one vo 5 (Kaka) + aan) 
n K K 
2I À k fG) — XXe E oa FG) Ym Yp0G 0p Eby £05) 
Figure 2 presents an example for multiquadric geometric processing, 
where six pass points shown as square box outlines have been employed. 
   
Figure 2 Example for multiquadric geometric processing 
Left: input image Right: output image 
2.4 Consideration of digital elevation models 
  
Geometric distortions due to topographic relief can be effectively eliminated, 
if a digital elevation model (DEM) with points DEM(X Hy)» m- 1,M are 
Y 
2m? 2m? 
given additionally to the pass points Pr k = 1,K. In this case in a first step 
the parametric sensor function is derived using the pass points Py /4,5/, and 
second the image coordinates Xn? Y Am of the DEM are derived from this func- 
m?! om Hn as input data. The total set of points P, * DEM, is 
then employed for the geometric processing. 
tion using the X 
2.5 Generation of thematic data bases 
  
With the help of digital image processing digital data bases can be obtained 
from existing maps. In a first step it is necessary to convert the (analog) 
map into digital format, i.e. to "scan" the map. Denoting the coordinate sys- 
tems as in Figure 35, then a relationship between the rectangular coordinate 
system X, Y of the map and the scanned map coordinate system X4,Y4 must be 
16 
e 
  
Scanr 
Figu 
defined 
tions) 
Y Jo X 
tion of 
is comr 
(50m) 2 
fines 2 
locatic 
jectior 
via equ 
ily con 
d(X1, Y: 
is repe 
tion oi 
Figur 
(a r8 REM