4.6 Filtering 
Filtering operations that decrease noise, thus enhancing low frequencies, lead to an increase of 
the convergence radius and rate, an increase of the correlation coefficient and a decrease of the 
estimated oy. The gray level derivatives are also smoothed, the normal matrix elements 
decrease, the inverse elements increase and the solution vector elements generally increase, 
depending on the effect of filtering on the right hand side of the normal equations. A 
comparison of the convergence rate of filtering versus no filtering is shown in Figures 3 b), 3 c). 
Median, local average and edge enhancing smoothing were examined. The local average gave 
the best and faster results. A 3 x 3 mask was used. A larger mask would in most cases lead to an 
even faster convergence, but there exists the danger that the signal, if its content is poor, is 
washed out. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
NO LOSS 
FILTERING| FILTERING| DIFFERENCE| FACTOR 
(1) (2) (2) - (1) CIN 26 ) 
Number of iterations per point 5.0 3.9 -1.1 -22 
CPU time per point (sec) 8.6 7.6 -1.0 -11 
Difference to bundle heights (cm) 1.3 2.2 + 0.9 +69 
az | Difference to bundle heights (%. hg) 0.016 0.027 + 0.011 " 
l| | Equivalent x-parallax clearance (um) 1.2 2.0 4 0.8 n 
05m Max difference to bundle heights (cm) 3.0 5.2 +2.2 +74 
Max difference to bundle heights (%. hg)| 0.037 0.064 + 0.027 , 
Equivalent x-parallax clerance (um) 2.7 4.7 +20 " 
Correlation coefficient 0.85-0.99| 0.91 -1. -- 
Number of iterations per point 13.3 8.8 45 - 34 
CPU time per point (sec) 29.7 20.5 - 9.1 - 31 
Difference to bundle heights (cm) 2.8 3.1 +03 +9 
AZ Difference to bundle heights (%. hg) 0.035 0.038 + 0.003 " 
Il Equivalent x-parallax clearance (um) 2.6 2.8 +02 " 
1.25m| Max difference to bundle heights (cm) 8.0 9.8 +18° +23 
Max difference to bundle heights (% hg) 0.098 0.120 + 0.022 * 
Equivalent x-parallax clerance (um) 7.2 8.9 + 1.6 " 
Correlation coefficient 0.77 -0.991 0 88- |. > pin 
  
  
  
  
  
  
  
  
Table 2. Filtering versus no filtering 
Table 2 gives the comparative results with and without filtering. It is obvious that the use of 
smoothing is particularly beneficial when the height approximations are not good, by cutting the 
number of iterations and processing time by about one third. The difference between the 
average difference to the bundle heights with and without filtering is less than 1 cm, and it 
decreases as the height approximation deteriorates. 
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