A 
   
  
  
  
  
  
| 
| | 
| 
| 
) | 
| 
| 
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define nl 
: 4 
no no yes no 
Figure la: Illustration of zero-sample and first densification 
By the next sampling run, a partial grid densification reduces by half 
the grid spacing of the previous run. Again the second differences at 
triplets of  equispaced points are checked against the threshold. The 
positions are defined accordingly for the next run of higher densifica- 
tion, and the next run is initiated. 
ELT 
  
4 
-* 
  
  
  
  
  
  
  
  
| 
3- J 
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4 | | 
2 | 
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14 J 
| | 
o4 a + $ 
yes yes no 
Figure lb: Illustration of second densification 
Sampling is terminated when either all second differences are smaller 
than the threshold or the pre-specified maximum number of runs has been 
reached. The resulting incomplete grid has locally a finest spacing of 
A . and globally a coarsest spacing of A = v MM os If rr is .the 
min o min 
number of executed densification runs. 
PS involves thresholding. The positions of sampling are therefore input 
dependent and, as such, PS is not a linear system in contrast to ES. 
Strictly speaking, the concept of transfer function, as utilized for ES, 
is not applicable to PS. The question is whether a "transfer function of 
PS" and the above plain estimator for Os would nevertheless be of some 
help in assessing the accuracy of a DEM obtained by PS. 
Applying PS followed by linear interpolation to sinusoids sin(2mvx) with 
different frequencies vé(0, 1/2] and computing a transfer function just 
as for ES 
$ ons here 
H(v, T, r 1- 2"e (C v, T, r) 
leads to a function as shown in figure 2. The function is composed 
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