International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
4.2 Object space 
Due to simulated systems with non-real values the evaluation of 
the systems interior and exterior accuracy is based on the 
assumption that the simulated values vary within their standard 
deviation and therefore each random modified bundle 
represents a possible real bundle configuration. The systems 
exterior accuracy is represented by the error of length 
measurement (LME) of distances with respect to calibrated 
reference scales. The particular characteristics of the LME 
concerning the verification of optical 3D-measurement systems 
are described at VDI/VDE (2000). With respect to the example 
bundles, which are used for the simulation process and the 
analyses, the following LME are based on the reference 
testfield of our institute (Figure 11, interior cube). 
  
  
  
  
  
Figure 11. Photogrammetric testfield 
The cube contains within a range of approx. 1m? 14 reference 
targets, which are calibrated by a CMM, therefore 92 reference 
scales for analysing purposes. The accuracy of the reference 
scales represented by 3D-coordinates XYZ resulted in 
RMS xyz [Ref] = 0.015mm. With respect to the used camera 
system (Kodak DCS 645 M, example Table 1) and the network 
design an interior accuracy of one bundle can be expected as 
RMS xyz [ObSp] = 0.040mm (7). 
  
RMS, ,,,, = J[RMS(X)F + [RMS(Y)] + [RMS(Z)] (7) 
(XYZ) 
Because LME are influenced by both uncertainties, this results 
to an expected range of LME of +601m for 1c, +120um for 26, 
+180um for 30. 
  
LMEof 196 simulations (60 images per bundle) 
01 A. — MÀ - Mn - à d 
0.08 + 
    
    
* uw x 
il t —— rr 
  
  
distanc e [mm] 
  
Figure 12. LME of 196 simulations 
  
LME of 195 simulations with RAD VAR -mod fication (60 images p er bundle) 
    
  
LME [mm] 
= 
& 
e 
= 
-0.15 Eo eM A 
distance [mm] 
  
  
  
Figure 13. LME for 195 simulations (RADVAR-modification) 
  
  
  
  
  
  
  
  
  
  
  
LME of input bundle (60 images) 
0.080 + 4 Lu 
0.060 + y 
0.040 s : # & + 
„+ + 
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ta ++ = Hi nete 
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= 002 43 200 an etek FET "aber 1200 
-U. EAE A i E N 
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+ ET 
-0.060 mr 
distance [mm] % 
Ja i D P Me ee ae 
  
  
  
Figure 14. LME of 2 results and overlaid InputB LME 
Figure 12 shows the resulting LME for 196 successful random 
bundles of each 60 images. The remaining LME result within a 
range of £100um. Regarding the simulated bundles considering 
RADVAR-modification (Chapter 3) the LME result in a range 
of £150 um (Fig. 13). Due to a high number of LME values the 
differentiation and analysis within one comparative diagram 
cause difficulties. Therefore 2 results (crosses) are exemplarily 
illustrated in Figure 14. These two diagrams are overlaid by the 
LME of the input bundle (InputB) that are displayed with dark 
dots. 
Summarizing the output values of the reference scales to a 
histogram, subdivided into 7 equal classes, the distribution 
results in an approximation of Gaussian distribution curves 
(Fig. 15). 
  
histogram of reference scales of 200 simulations 
     
  
count of scales in class 
1 2 3 4 5 6 7 
histogram class x of 7 
  
  
  
Figure 15. Histogram of reference scales 
Due to the normal distributed input values this resulting 
distribution was expected. Hence the simulation process works 
properly for normal distributed random modified bundles. This 
effect is confirmed by resulting normal distributed output 
values for reference points with respect to the point of origin. 
   
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