International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004 
  
that this scanner cannot be used for photogrammetric tasks 
without additional geometric correction of images. 
Affine transformation was used as the second transformation 
model (eq. 3) 
X=al+tal*y+at"x 
(3) 
Y=bl+b2+#y+b3+x 
where: X,Y - grid point coordinate in plate coordinate system 
(in um) 
X,y - pixel coordinate of grid points 
ai,bi - coefficients 
Achieved RMSE based on residuals after affine transformation 
is about 30 um for each axis, with maximum errors up to 70 
um. Overview of error vectors after applied affine 
transformation is given at Figure 4. 
  
  
^g mni piu 108117 
Gem UU LLTT 
Mo 
  
  
  
Figure 5: Error vectors after collocation with filtering was 
applied. 
Affine transformation (eq. 3) has been used before collocation 
in order to remove trend. 
  
Scannin = ; Empirical 
B Affine Collocation pue 
parameters covariance 
  
My Mx My Mx | CovY | CovX 
(um) | (um) | (um) | (um) 
  
  
4 £24: x 
—3 100 um 
i 
Figure 4: Error vectors after affine transformation. 
  
  
As for the previous case, it can be concluded that errors still 
contain systematic part, but much smaller in magnitude 
comparing to the one after Helmert transformation. Also it is 
clear that this systematic influence is locally changing. Still, 
overall geometrical accuracy is insufficient for digital 
photogrammetric tasks. 
The third mathematical model used is previously described 
linear prediction by least square (collocation). Achieved RMSE 
based on residuals after collocation with filtering is about 4.2 
um for the first and 8.5 um for the second axis. Maximum error 
for any grid plate was not exceeding triple value of RMSE for 
that plate. 
Figure 5 represents error vectors after collocation with filtering. 
Random arrangement of error vectors might lead to conclusion 
that systematic part of an overall error is mostly eliminated. 
36.51 | 32.14 | 4.14 | 9.76 0.90 0.84 
  
38,73 |.29.90 | 392.1-9.70 | 030 0.85 
  
35.01 | 28.85 | 3.80 | 935 | 0.90 0.84 
  
35.40 130.261" 3.6] 928 | 0,90 0.85 
  
3847.| 29.80 | 3.54 | 0.234 | 0.91 0.85 
  
1200 dpi 3470 | 2731 | 3.51 | 376 | 090 | 0.54 
  
grayscale [3626 | 31.69 | 3.59 | 878 | 0.91 | 0.86 
  
35.04 | 28.85 | 3.61 372 0.91 0.86 
  
35.15 * 29.32 | 3.69 8.9] 0.91 0.85 
  
33.31 | 29.97 |} 398 8.70 0.91 0.84 
  
33.04 | 29.78 | 3.80 | 8.30 0.91 0.85 
  
38.24. 1 39.14 |- 335 S39 «3.09 0.84 
  
1000 dpi 33.01:71.29.71 | 4.69 | 345 0.86 0.83 
  
Grayscale | 34.33 | 29.62 | 4.48 | 8.63 0.87 0.82 
  
34.29 | 29.97 | 4.96 | 8.92 | 0.86 0.81 
  
1600 dpi 34.16 | 28.06 | 4.30 | 7.98 | 0.86 0.83 
  
Grayscale | 33.87 | 27.77 | 4.01 2 98 0.86 0.84 
  
33.71.1-27.70-1.3.90.] 7.46 1 0.87 0.84 
  
1000 dpi 53.67 | 2781 | 5.53 7.64 0.85 0.82 
  
RGB 32.06 | 27-41} 504 |. 7,37 0.86 0.83 
  
33.81 | 27.01 | 5.260 | 7.73 0.85 0.81 
  
1600 dpi 3335 |.27.66 | 4.14.1. 7.75 0.86 0.83 
  
RGB 33.92 | 28.29 | 4.48 | 8.40 | 0.86 0.81 
  
  
33.37 | 28.04 | 4,28 | 8.65 0.86 0.81 
  
  
Mauro | 34.67 | 29.01 | 4.17 [854 
  
Mmax 36.51 [32.14 65.23 | 9.76 
  
Mmin 3335 {2701 {-354 0 737 
  
  
  
  
  
  
  
Range 3.16 513 1.99 | 2.38 
  
Table 6: Parameters of the scanner geometric accuracy 
Table 6 shows the results of the scanner global geometric 
accuracy. RMSE values based on residuals after affine 
transformation and collocation with filtering are given. My 
shows RMSE based on residuals after coordinate transformation 
   
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