Kazuo Oda 
  
where differences of pixel values between the stereo pair images are summed up. 
where 
2.2 Evaluation Function 
and Ec 
We can 
  
   
  
where | 
Iorth x, y, EJ, 1, 
lorth x, y, E, I, 
: 23 Le 
Figure 1. Stereo Images and DSM 
We hav 
LL Eall 
Suppose that we have digital surface model (DSM) z = z x y , and that camera position P = x y z] and camera atti T 
tude T = T ] are unknown. We use notation of full absolute orientation parameters of the camera as below. 
E = > tp = T X y Z| (2) fa 
Camera coordinates P, of a point p = A y = x y ] on DSM can be described with P and T. 
where 
f 
a iv v "iz = 
PC b», 5, RT p-P 
where R T is the rotation matrix: 
1 0 0 cos 0 sin cos —sin 0 
RT - |0cos —sin 0 1-0 sin cos 0 (4) 
0 sin cos —sin 0 cos 0 0 1 
: iy ; ; ; : : This co 
Equation (3) and (4) give image coordinates P, pe On which point on the DSM x y z x y is projected: 
Partial « 
t 
! €x Cy 5 
CV = : ; = r Ar | 
Pont xy E | Yoh mU. e 
E y 
where c is the focal length of the image. 
where 
An orthoimage Jorth x y E I can be composed from the image / with the following equation: 
lorihbx y El 2 IP,xy E (6) 
For stereo pair images /, and 7, , two ortho images Zorth, and Iorth, can be computed by equation (6). 
If absolute orientation parameters of /, and I, are closer to the correct value, difference of two ortho image Zorth, and 
Iorth, should be smaller at each point on DSM. DSM based orientation calculates the parameters which minimize lli 
difference of two ortho images. 
The difference of image values between /orth, and Iorth,at p = T. yz x y]is: 
  
652 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.