Kazuo Oda 
  
P P hi^ : ; ; ; ; ia 1. 
2 and E" ^ jin equation (15) can be analytically determined with the equation (3) and (4). In digital image process. 
1 
  
  
  
  
  
I 8 ; 
ing image values are given by pixel values / x Ppix Ppnt . Thus ——— and —— can be denoted by following equa. 
: phtl pht2 
tions: 
5 n. I ul Pix! I, = Tpix2 Prix2 
Poht 1 Pix! Pphti Poht2 Prix2 LE. (16) 
L3 b uc ns ; A Prix] Ppix2 
PIX and -22 correspond to differential images in column and row directions. PP” and —P*- can be calculated 
pix! pix2 phtl pht2 
from the relationship between P i and P, nt » Which can be affine or projective transformation if optical distortion or 
X 
film deformation is negligible. 
2.4 Variation of Optimization under Restriction 
2.4.1 Optimization under Epipolar Geometry: Suppose that Epipolar geometry between the two images are known, 
i.e., relative rotation matrix &,,, and direction vector [ b, e] from the optical center of 7, to the optical center I, arc 
given. In this case the target parameters Eall have 7 degrees of freedom which is: 
Eall = [3 7 =r, P, L}= T ı ı 1% Yı2; j (17) 
t 
where L is a scale parameter. The absolute parameters E, = i T, f P, can be derived from the following equations. 
  
  
  
  
  
  
  
  
  
R T, Roi À 7] (18) 
t 
PoRL ORT, ran] +o, (19) 
. e 
Instead of equation (14), Fall can be expressed as follows: 
e … | © er I I, I, (20) 
Eall "L = d 
a FE, L E, E, L 
where 
E = 4; Fons n = Amy Poni E, I - Mas Phi? E; 
E; Puit, E; Pp E E, L ‘Poiuz fa L (21) 
2.4.2 Optimization with fixed parameters: Suppose that ith element value of Eall (E;) have been fixed and other 
unknown parameters should be optimized under this condition. This problem can be solved simply by setting O to € in 
i 
t 
Jacobian matrix. The element A A ji is also set to 1 in convenience, to avoid deterioration in rank of matrix '4 A 
in the equation (11). This derives that E; — 0 and optimization procedure does not renew the element £;. 
This situation can be applied to conditions with combination of any fixed parameters, for example, when absolute paran 
eters of one image are known, or when two optical centers are measured by, for example, GPS. It is recommended to us 
any restriction to compute DSM based orientation since restriction brings robustness to the result. 
  
654 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
  
3. TEST 
3.1 Test 
The algor 
the first s 
ing point 
geometry 
rithm on t 
computed 
was used 
Figure 3 1l 
the figure 
orthophot 
3.2 Precis 
The precis 
precision c 
tests result 
method is |