the influence factor is given by 
pi m ea HBS Bay) By] (16) 
(17) 
This measures the maximum relative increase in uncertainty 
of the estimates y if observation group % is omitted. x 
Is the covariance matrix of the estimates from an estimation 
without observation group i. 
and the test statistic 
T; 2 Me TXD eo (18) 
with e*" being the residual vector of estimation group 4 and 
xe the corresponding covariance matrix. A gross error in 
the observation group ¢ can be detected with a significance 
level œ by checking 
(i) 
Ti» x (a, n) 
with 
n — Number of fiducial marks in observation group : - 2 
a = significance level e.g 99.9% 
The goal of the sensitivity analysis is to get one overall ob- 
jective quality measure which evaluates the success of the 
automatic fiducial mark location. 
Equation (13) shows the influence of the observed positions 
of the fiducials in the image to an arbitrary function of the 
unknowns, namely the transformation parameters from the 
plate system to the pixel system. Thus the maximum influ- 
ence (worst case) of an observation group to a transformed 
point using the estimated transformation from image system 
to the pixel system in pixel is 
N viai OT (8) - MAT (04) (19) 
where a; is the variance of the adjusted observations. 
5.2 AIO: A Traffic Light Program 
There are two critical matching tasks within the AIO: these 
tasks are critical in the sense that they may fail for some 
reason. The first is the detection of the orientation of the 
image, and the second is the localization of the fiducial marks. 
The result of both matching tasks is evaluated and classified 
into one of the three categories of the traffic light. 
For the evaluation of the orientation detection we use a hy- 
pothesis test to check whether the maximum correlation co- 
efficient prmax1 IS significantly different from the second max- 
imum Pmaz2. The normalized test statistic is 
Pmazi — Pmaz2 
T= ~ N(0,1) (20) 
gà maa 7) aad 
TL + TL 
Using this test statistic, the controlling of the traffic light can 
be achieved by applying the following different significance 
levels o: 
green : T € N(a = 0.05%) 
yellow Ní(o 0.0594) « T« N(a 019) : (21) 
red UT 2UN(o 09$) 
750 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
For the final evaluation of the the localization of the fiducial 
marks we use the sensitivity analysis. The maximum influence 
of an observation group on a transformed point using the 
estimated transformation from the image system to the pixel 
system (equation 19) is used to control the traffic light: 
green, Vas < OS pixel 
yellow 0:5 pirel < Vmar < 1 pizel (22) 
red : Vmaz 2 L pixel 
The test statistic shown in equation 18 is used to inform the 
user of possible incorrect fiducial mark localizations. 
Example: 
      
     
   
p 
Bz 
Figure 8: A failed localization of a fiducial mark 
Figure 8 shows a negative image of a fiducial mark. The black 
cross marks the incorrect localization of the fiducial mark. 
Ti m ó; dio 
1-11 | 070 2.91 | 2.31 
0.16 | 0.65 1^0.38 | 2.59 
136-1070 | 3.55 | 2.81 
1.01..| 0.65 | 2.44 1.2.50 
2.20 1-0.70 1: 5.74.4 2:81 
3.73 | 0.65 | 8.99.1.2.59 
1.71 1.0.70 | 4.47 | 2.81 
1.20 1 0.05 |.2.08 | 2.59 
Table 1: Sensitivity values; number 6 is the fiducial mark 
shown in figure 8 
  
ONC DWN HH, 
  
  
  
  
Table 1 shows the corresponding result of the sensitivity anal- 
ysis and the normalized test statistics for each single fiducial 
mark. In this case the maximum influence of an observation 
group Vmaz was 0.9 [pizel], which indicated an error. Fidu- 
cial number 6, having the largest test statistics, is the one 
shown in figure 8. 
6 AIO IN A PRODUCTION ENVIRONMENT 
The development was a joint cooperation between the In- 
stitute of Photogrammetry, Bonn University and Carl Zeiss, 
Oberkochen, Germany. The presented AlO is part of the Dig- 
ital Photogrammetric Workstation (DPW) PHODIS (Pho- 
togrammetric Digital Image Processing System). 
The product family PHODIS from Carl Zeiss company uses 
several automatic processes to support the daily work with a 
(DPW). Besides the AIO there are several other automatic 
    
  
    
    
    
     
    
   
  
    
    
    
    
  
  
  
     
    
  
  
   
      
    
   
   
   
   
   
   
   
   
    
   
     
    
    
   
  
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