(4) 
ition of 
uation 4 
M. ZM) 
(X,Y,Z) 
ving 12 
(5) 
alent to 
ove we 
entation 
ng rays 
entation 
ereopair 
e model 
ined, if 
pace. 
ADJA- 
on four 
Che first 
second 
ird and 
nship is 
els (See 
affine 
code 
2,1m2) 
ple 
transformation (Equation 5) is satisfied between the first 
stereo model space (X M1, YM1, ZM1) and the object 
space (X, Y, Z) in the form 
X Mi = BX + BY + B+Z + Ba 
YMi = BsX + BgY + B7Z zi Bag (6) 
ZM1 = BoX zi BioY + BZ + B5 
or inversely as 
X = C,XMi1 + C) YM1 + C3ZM1 + Ca 
Y = CsXm1 + CeYm: + C7ZM1 + Ca (7) 
Z = CoXM1 + C1oŸM1+C11ZM1+C12 
The same can be described between the second stereo 
model space (XM2, ŸYM2, ZM2) and the object space 
(X, Ÿ, Z) in the form 
X M2 = DX + D5Y + D3Z zn Da 
YM2 = DsX pH DgY + D7Z + Dg (8) 
ZM2 = DoX + DioY "ES DZ + Di, 
or inversely as 
Ne E,XMi + E> Ya 1 + E3ZM1 re E4 
Y = EsXm: + EsYm: + E7zZM:1 + Es (9) 
Z = EoXm1 + EsoŸMm:+E11ZM1+E12 
By substituting Equation 9 into Equation 6, we get 
the relationship between the first and second stereo 
models in the form 
XM1=F1XM1i+F2YM1 + FaZm: + F4 
Ym:=FsXMm:+F6Ym1 + F7ZM1 + Fa (10) 
ZM1=F9XM1+F10ŸM1+F11ZM1+F12 
which coincides with the general affine one-to-one 
correspondence (Equation 5) between two three- 
dimensional spaces. It means that the first and second 
stereo models can be connected by the general 
three-dimensional affine transformation. 
TRANSFORMATION OF CENTRAL-PERSPEC- 
TIVE IMAGES INTO AFFINE ONES 
The satellite CCD camera conventionally has an 
extremely narrow field angle. Thus, the conventional 
orientation approach is not effective due to very high 
correlations among the orientation parameters. On the 
other hand, the orientation theory of two-dimensional 
affine imagery may be effectively applied to the 
analysis of satellite CCD camera imagery, if the 
central-perspective images can be transformed into 
affine ones. Also, this transformation will be 
performed in a following way. 
Let the ground surface be flat and a central-perspective 
613 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
    
   
   
   
   
  
    
    
  
  
  
    
    
    
    
     
     
  
    
     
    
   
     
    
   
    
   
   
   
   
   
    
   
    
photograph be taken with the rotation angles (jj and p. 
The reference coordinate system (X. Y. Z.) is selected 
- as a right-handed, rectangular Cartesian system with its 
origin at the projection center of the photograph and 
with its X - Y plane parallel to the scaled ground 
surface, as is demonstrated in Figure-4. Further, the 
/ 
Z 
  
image plane 
Figure-4 : transformation of a central-perspective 
image into an affine image 
photograph 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. 
Y Le) of an image point D(X, y) of the central- 
perspective photograph are expressed with respect to the 
reference coordinate system 1n the form 
^ 
^ 
V1 =} FO" (^99 
Xp cos à O sin $ [oss 
-sin® 0 cos ® 
0 cos w -sin val] 1) 
Osinw cosw 
in which c denotes the principal distance of the picture. 
Also, the principal point H of the central-perspective 
picture is given with respect to the reference coordinate 
system as 
Xy -c'sin i cos w 
Yul = C'Sin (0) (12) 
7 -C* cos th cos w 
Further, Let P(X 5 Y, Z) denote the point at which 
——» 
the ray Oap intersects the scaled ground surface. 
The three-dimensional coordinates of this point can be