FT ^ s 
eui 
  
e 
co 
  
‚© 
  
Probality 
© 
A 
  
IN 
  
  
  
  
0.1 1.0 10 
B = step size/rms noise 
Fig 6.2 
Probability of correct assignment of digital value correspondning to 
the noise free signal within +0, t1, ... +9 digital levels. The signal 
is uniformly distributed over the quantization intervals and 
contaminated by gaussian noise of value O. The probabilities are given 
as a function of B ( after Billingsley, 1975 ). 
6.1 Probability of Separating Two Areas of Different Brightness 
In section 3.3 it was suggested that rather than using functions based 
on human vision when determining the cut-off frequency of the image, 
properties of the imaging and digitizing system should be used. In 
this context it is of interest to be able to decide whether two areas 
in the image with different grey levels can be resolved. 
We can estimate the probability of resolving two areas in the image 
with an average transmittance difference AT ( Billingsley, 1975 ). 
Both areas are supposed to be contaminated by gaussian noise equal to 
6. The areas are resolved if AT>0, not resolved if -o « AT/2« 0 and 
spuriosly resolved if -e««AT/2«-o. Spuriously resolved means that we 
get an indication that they are different although they are not. The 
probabilities are given by 
P(resolve)=[1+erf(AT/20-1)]/2 (6.2) 
P(unresolved)= [erf(AT/20+1)-erf(AT/20-1)]/2 (0 6.3. J 
P(spurious) = [1-erf(AT/20+1)]/2 (6.4 ) 
In the expressions above AT can be related to AD in section 3.3 and 
3.4. We can analyze whether the digitizer will be able to resolve a 
difference in transmittance corresponding to the difference in density 
we used for deciding the cut off frequency and the sampling interval. 
150