Additionally, less iterations are required and the DTM 
production time is decreased. More details on this 
matching approach and extended tests are published in 
Baltsavias and Stallmann, 1992. 
6. DIGITAL ORTHOPHOTO GENERATION 
The object to image PMFs were used to transform a DTM 
into SPOT images for orthophoto generation. The PMFs, 
while being very accurate, offer tremendous advantages 
regarding speed, a crucial factor for orthophoto 
production. The speed can be further increased by 
suitable factorisation. As an example let’s consider the 
basic object to image polynomial 
F(E,N,h) = a'p (1) 
with 
a -(1 h E N hE hN E? EN 
; (2) 
N? hE? E° E°N h’EN hE) 
p. z (p Py +» 12290) (3) 
involving 30 multiplications and 13 additions. By a 
suitable factorisation its form changes to 
reference image 
image ray 
  
  
   
  
    
      
. J 
{ epipolar plane Lf 
(2 
CSP TETE PES ST e 
SOS SOS LS FL SL LS 
reference el 
Zi + AZ 
Y Zi- AZ 
PTI ITI ITT ITI TITS 
p; +h (p,+ Eps + Npg) 
-E(p4* E(p; * hp Ep, + Np12)) (4) 
+N (p4, + Np, + E (p,+h (hp,3 + NP4,4))) 
involving 14 multiplications and 13 additions. Even 
larger computational savings can be achieved by using 
incremental updating of the results of the previous pixel 
within the column (or row). Updating in column direction 
is faster than row updating as there are less terms 
involving N than E. The first pixel of each column can be 
updated from the results of the first or last pixel of the 
previous column. The implementation of this approach 
involves 5 multiplications and 8 additions, and for the 
first pixel of the columns 7 multiplications and 14 
additions. The respective number for the extended PMFs 
is 5 multiplications and 9 additions, and 8 multiplications 
and 16 additions. À speed increase of factor 3 in 
comparison to equation (4) has been achieved. An 
orthophoto of a whole SPOT scene, using bilinear 
interpolation, needs only 15 min. on a Sparcstation 2. 
This is faster than other much more expensive digital 
orthophoto systems that utilise special hardware (the 
PRÉSM workstation of ^S for example needs 20 min.). 
The accuracy of the orthophotos produced by the PMFs is 
very good. In Baltsavias et al., 1991 accuracies (RMS) of 
5m -6m are reported. Hammon, Jensen, Wallen and 
Assoc., a California based company that has integrated 
our software within ARC/INFO, made tests with 8 SPOT 
scenes having big height ranges (up to 60 m - 4200 m). 
ossible deviation 
orm straight 
(“epipolar”) line 
straight (“epipolar”) line 
   
        
  
    
KARINA REN 
   
9 8 ws 
  
Figure3 Approximation of epipolar geometry for SPOT images 
362