Ilkka Niini 
  
the constraint 5 could not be formed between the observations. However, it can be noted that the maximum redundancy 
was obtained and, hence, all image data could be used in the physical adjustment version. In the common data cases, th 
same redundancy (358) was obtained with all three adjustment methods. 
  
| Cs [AB CID] 
Projective 1 | 87 | 428 | 109 | 319 
Projective 2 | 97 | 541 | 109 | 432 
Projective 3 | 77 | 467 | 109 | 358 
Physical 1 | 97 | 522 | 66 | 456 
Physical2 | 77 | 424 | 66 | 358 
Bundle 1 97 | 813 | 357 | 456 
Bundle 2 | 77 | 655 | 297 | 353 
Table 2: The characteristics of the testfield cases. A=number of object points in adjustment, B=number of equations, 
C=number of unknowns, D=redundancy. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
5.2 Results 
First, the cases with the same data and redundancy were studied (cases Projective 3, Physical 2, Bundle 2). The RMSE 
between the resulting 3-D models from these cases are shown in Table 3. In these cases, the results were the same y 
to the used iteration termination limit (here 1 - 107? units). Other adjustment results of these cases were also the same, 
and, therefore, these results are presented only once in consequent tables 4, 5, 6, and 7, with the title 'Common dan 
cases'. Only the results from the physical and bundle adjustments were expected to be identical, whereas slightly differen 
results were expected from the projective case. However, as the data and redundancy was the same, the final results were 
also the same. This proves that the computational details (use of constraints, linearization, calculation order, etc.) in 
different adjustment methods are in coherence, because similar results would not have been possible otherwise. It also 
demonstrates that the bundle method is not always superior compared to other methods like the ones presented in this 
article. 
  
  
  
  
  
| Cases | RMSEX | RMSEY | RMSEZ |RMSEXYZ | 
Projective 3 - Physical 2 | 5.788-10-! | 6.592 10-9 | 5.54610? | 5.992.101? 
Projective 3 - Bundle2 | 6.833 10-1? | 7.033 10? | 5.606 -10 9 | 6.521.101? 
Physical2-Bundle2 | 1.583 -10-" | 7.304 -10-!" | 1.116 -10-"° | 1.195-10-"© 
  
  
  
  
  
  
  
  
Table 3: Pairwise difference between the three models (in mm) in cases where the data and redundancy are the same. 
The standard error of the adjustments, and the RMSE's between the 3-D models and the known object are shown in Table 
4. It shows that the cost of the missing data and equations in the projective case, compared to the bundle results, is 
relatively small. The best projective RMSE value was 1.0524 mm, whereas the corresponding bundle result was 0.952] 
mm, i.e. projective results are worse by a factor of 1.1 only, compared to the bundle results. If the new constraints 
(equations 1 and 5) were not taken into account (as in case Projective 1), the projective result was about 1.3 times worst 
than the bundle value (1.2176 mm/0.9527 mm). Thus, these constraints make the results clearly better. 
The 3-D model RMSE from the physical adjustment was exactly the same as the corresponsding bundle value (0.9577 
mm). This was expected, because the data and redundancy were also the same. 
The values of the exterior orientation parameters are not presented here because only the accuracy of the object modd 
was interesting. The final interior orientation and non-linear parameters are presented in tables 5, 6, and 7. They are 
also same in the physical and bundle cases. The projective results are also very good. For example, the principal point 
co-ordinates from Projective 2 case differed from the bundle result not more than about one pixel, except the zoom 
focal length which was about 14 pixels too short. The results from the first projective case were quite similar, despite th: 
lack of observations. 
  
  
  
  
  
  
  
|. Case | so (pixels) | RMSE in XYZ (mm) | 
Projective 1 0.2994 1.2176 
Projective 2 0.2925 1.0524 
Physical 1 0.2918 0.9527 
Bundle 1 0.2918 0.9527 
Common data cases 0.2967 1.0580 
  
  
  
  
  
Table 4: Standard error of adjustment (59), and the model accuracy (RMSE). 
  
648 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
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