SPACE TRIANGULATION USING AFFINE TRANSFORMATION 
ATSUSHI OKAMOTO 
KYOTO UNIVERSITY KYOTO JAPAN 
COMMISSION III 
ABSTRACT 
If the DLT method is applied for space triangula- 
tion with satellite photographs, high correlations 
arise among the orientation unknowns due to very 
small height differences in the terrain for the fly- 
ing height of the platform. This difficulty can 
however be overcome by using ground point co- 
ordinates calculated by means of affine transfor- 
mation as the initial values for the iterative solu- 
tion. This approach is tested with simulated ex- 
amples and is revealed to have a fairly good accu- 
racy. 
INTRODUCTION 
The DLT method(Abdel-Aziz and Karara(1971)) 
is a general orientation approach of photographs. 
This method is usually applied for the analysis of 
non-metric photographs. Employing the DLT ap- 
proach for the analysis of satellite photographs, 
the attained accuracy may not be so high due to 
very high correlations among the orientation pa- 
rameters, because height differences in the pho- 
tographed terrain are very small in comparison 
with the flying height of the platform. In order to 
overcome this problem, this paper proposes an 
orientation method of adopting ground point co- 
ordinates as the initial values for the iterative so- 
lution, which were calculated by means of an ori- 
entation theory of photographs based on affine 
transformation(Okamoto, et al(1989,1991,1992)). 
Also, the proposed method is applied for space tri- 
angulation with simulated satellite photographs 
taken consecutively in a convergent manner. The 
camera is assumed to be a non-metric one. Fur- 
ther, the analysis of satellite CCD camera im- 
ageries with a very narrow field angle is per- 
formed using the orientation theory based on 
affine transformation. 
OUTLINE OF THE PROPOSED ORIENTATION 
METHOD 
The basic theory for analyzing affine imageries 
346 
has first been constructed by Okamoto(1989) and 
in detail explained in the paper by Okamoto, et 
al(1991,1992). However, this theory cannot be 
applied for the analysis of conventional pho- 
tographs without transforming the central-per- 
spective imageries into affine ones. Thus, this 
transformation will first be discussed. 
Let the ground surface be flat and a central-per- 
spective photograph be taken with the rotation 
angles o and 9. The reference coordinate sys- 
tem (X,Y,Z) is selected as a right-handed, rectan- 
gular Cartesian system with its origin at the pro- 
jection center of the photograph and with its X-Y 
plane parallel to the scaled ground surface, as is 
demonstrated in Figure-1. Further, the photo- 
graph is considered to intersect the scaled ground 
surface in such a way that its principal point H lies 
on the surface. The three-dimensional coordinates 
(Xp, Yp.Zp) of an image point p(x,y) of the central- 
perspective photograph are expressed with respect 
to the reference coordinate system in the form 
  
  
  
Xp cose Osing |[1 O0 0 X 
35.451..0..1.—0 0 coso -sino || Y | (1) 
Zp sing 1 cose [LO sinw coswlL-C 
    
  
y 
Da (Xa, ya) 
   
  
Figure-1 : transformation of a central-perspective 
photograph into an affine one 
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