International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
Table 2: Number of iterations used by the four algorithms 
for each camera pair. Failure to converge in 20 iterations 
is indicated by a dash. c was below 11 microns for all 
converged cases. 
  
  
  
  
  
  
  
  
Pair Number of iterations 
# Stations  Alg. IU Alg. ID Alg.2U Alg. 2D 
1 5, 14 — 12 8 7 
2 5,13 — 9 — 9 
3 13, 14 4 5 4 5 
4 4, 25 3 3 3 3 
5 14, 15 3 3 3 3 
6 28; 31 5 7 5 7 
7 26,27 4 4 4 4 
8 15, 28 6 6 6 6 
9 15. 31 4 4 4 4 
10 4, 26 3 3 3 3 
11 4. 5 4 4 4 4 
12 14, 28 4 4 4 S 
3 14, 31 4 4 4 4 
14 4, 30 4 4 4 4 
15 4, 29 4 4 4 4 
16 5, 29 4 4 4 4 
17 5, 30 3 3 3 3 
18 24, 25 11 6 10 6 
19 4, 24 4 4 4 4 
20 25, 26 3 5 5 5 
21 4, 27 3 3 3 3 
22 29, 30 c --H — — 
23 27,28 4 4 4 4 
24 8.12 3 3 3 3 
25 12, 13 o v -— 
26 [2. 14 4 4 4 4 
27 26, 28 4 4 4 4 
28 13, [5 — 8 — 8 
29 24, 26 4 4 4 4 
30 3.15 4 4 3 3 
31 4,28 4 4 4 4 
32 [2°15 8 9 
33 23722 4 4 4 4 
Total # failures 6 2 5 2 
1. Damped algorithms converge, undamped fails. Case 
2, 28, 32. 
2. Damped algorithms use fewer iterations. Case 18. 
3. Undamped algorithms use fewer iterations. Case 6. 
4. All algorithms differ. Case 1. 
5. All algorithms fail. Case 22, 25. 
6. Small differences. All other cases. 
Examples from classes 1—4 are illustrated in figures 2—5. In 
Class 1 (Figure 2), the undamped algorithms overshoot the 
target in the first iteration and never recovers. The damped 
algorithms take smaller steps (initially down to o = 1/16) 
but converge. In Class 2 (Figure 3), the undamped algo- 
rithms overshoot the target, but converge, although slower 
than the damped algorithms. In Class 3 (Figure 4), the un- 
damped algorithms are faster than the damped algorithms. 
Finally, in Class 4 (Figure 5), the constrained algorithms 
are better than their unconstrained versions, with faster 
592 
  
9 
Algorithm 1U, 2U 
  
e Algorithm 1D, 2D 
Figure 3: Algorithm behaviour for Case 18, all points. The 
undamped algorithms overshoots the target, but converges. 
The damped algorithms take shorter initial steps and con- 
verge faster. 
convergence for Algorithm 2U than 1U and convergence 
for Algorithm IU despite failure for Algorithm ID. 
Further analysis of the Class 5 cases reveal that in case 22, 
the starting approximation algorithm suggest that the two 
cameras were 45 cm apart and that one point was behind 
both cameras. Modifying the starting approximation by 
mirroring that point through the midpoint of the baseline 
produced convergence in 9 iterations for the damped algo- 
rithms, but still failure for the undamped algorithms. In- 
creasing the maximum number of iterations revealed that 
in case 25, the damped algorithms converge in 22 itera- 
tions. 
The optimisation results for the 500 x 33 subset optimisa- 
tions are shown in Table 3. The results for each case are 
similar to their “all point” cases, but with larger differences 
between individual cases. On average, the constrained al- 
gorithms are marginally better then the unconstrained algo- 
rithms. The damped algorithms have equal or lower failure 
percentage for all cases, but the difference varies substan- 
tially. In case 1, 90% of the failures are eliminated by the 
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