iat 
(3.1) 
trices Dy 
that every 
rove the 
efficiency 
3D object 
| (k+1)th 
trix 
wu (3.2) 
r (k+1)th 
(3.4) 
. with its 
(3.3), the 
ans when 
ation is 
ie. defined 
lar image 
on to the 
D object 
vo images 
Dz-(A* AyFASA;)' 
(aik*aik aik*bik. aik*cik 
2 
: 4 
= (X lja,k*buk büuk*bik bi.k * crx | ) 
= 
— 
1 
ak"cik bik*cik cik*Cci,k) 
In general, if there are four square matrices A, B, C 
and D, and D = B°, the following holds 
AB 
n ) ; = 
D c 
THA + A'B(C-B'A'B)'B'A + 
(C - B'A* B)') 
Similariy, the precision criterion will be : 
Tr(D»5)=(S*,+ S^ysin'c; TH /(sin“ à ; *sin^ a ) 
= minimum (3.3) 
where 
i and j are IDs of two intersecting images; 
S; is the distance between i-th camera and the target 
p 
S; is the distance between j-th camera and the target 
p 
cj is the space intersection angle between two 
observations; 
H;; is the distance between the target P and baseline 
vector ij; 
a ,is the space intersection angle between i-th 
observation and baseline vector ij; 
a ;1s the space intersection angle between j-th 
observation and baseline vector ji. 
3.2 Reliability Criterion 
A statistical hypothesis test can be used to detect 
model errors by examining the difference in the 
observation Equation (2.5) 
dL 1=(Axs1Pi-Lit1) ^ N (A Li. DriiztAga Di Asa). 
(3.6) 
  
    
   
   
   
   
  
      
     
    
     
   
    
    
  
   
   
   
   
   
    
   
  
  
   
   
     
    
    
   
and a further 7? test can also be applied 
dL'a (Di * Aca Di Aa)! dbia z^ Q. 87). G.7) 
A boundary value |AL: +1| may remain undetected by 
AL (Dur + Avr Du Aa)! A Lan 8, (3.8) 
where $.* is a non-centrality parameter. It can be 
determined by a , the significance level, and 7. the 
power of the statistical hypothesis test. The value of 
the undetected model error AL, dependents 
mainly on matrix (Di; + Ay Dix Ax). Therefore, 
we define (Dij. * Aka Dy Ax) as the reliability 
criterion matrix. 
The reliability criterion is then set as 
Tr(Di1 + Aya Dy. Al) = minimun. (3.9) 
4. EXAMPLE 
So far the precision criterion has been implemented. 
The results with the combined precision and 
reliability are to be reported. The above precision 
optimization criterion was applied to select two out 
of six images acquired by the VISAT mobile 
mapping system for intersecting the object (Figure 
4.1). The camera positions are numbered as 2.0. 2.1, 
3.0. 3.1. 4.0 and 4.1. The following table gives the 
optimization results of two tests initiated with 
different image pairs. 
To some extent. the efficiency of the automatic 
optimal image selection procedure depends also on 
the reliability of point matching techniques. In this 
system, the distance between the target and camera 
exposure stations is limited to 65m. Further more, 
potential images for selection are limited to 3 
neighboring image pairs. Thus, the mismatching rate 
can be greatly reduced and the efficiency of the 
optimization can be improved. 
  
  
  
  
  
  
  
  
  
  
Test Camera 1 Camera 2 Xn) Y(m) Z(m) 
Initial pair 3.0 33 474617.209 5183959 219 69.935 
Optimal pair 4.0 2.1 474617.640 5133959 397 69.884 
Initial pair 4.0 4.1 474617.042 5133959 063 69.804 
Optimal pair 4.0 2.1 474617.623 5183959.411 69.849 
  
  
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996