15 
  
15 
  
13 
butions. RMS 
e number of 
ction process. 
reased as the 
ance between 
d number of 
which seldom 
ns was good 
it was slowly 
elected points 
ceeds. 
in Fig. 2. The 
accuracy of X 
tracted points 
  
» 
  
RMS error [cm] 
  
  
  
2 3 5 10 15 
Number of selected points 
b) 
wn 
  
N U 4 
RMS error [cm] 
- 
  
  
Number of selected points 
C) 
  
N ®% 4 — tA 
RMS error [cm] 
— 
  
  
2 3 5 10 15 
Number of selected points 
  
| —e— Full ——spl4 — — spl_all2 —O— spl2 
  
Figure 4. Reducing completeness of the observations. RMS 
errors in the check points as a function of the number of 
selected points in each tie point area. (Full: full completeness, 
spl4: splitting to 4-neighbouring combinations, spl_all2: 
splitting to all possible pairwise combinations and spl2: 
splitting to 2-neighbouring combinations). In case spl2, the 
RMS errors in Z were in the order of 10 cm and are not shown 
in the figure. 
had significant influence on the accuracy of Z, but only up 
to a certain limit. 
e It looks like 15 points per tie point area was close to an 
optimum under these conditions, giving RMS errors: X: 2.0 
em, Y: 2.9 cm and Z: 3.6 cm. Any further increase in the 
number of points did not give better results. 
3.2.2 Using 5x5 tie point area distribution 
A 5x5 tie point area distribution was tested to see if it has any 
effect on the accuracy of the block. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
The RMS errors, when using all observations were: X: 2.2 cm, 
Y: 3.1 cm and Z: 3.6 cm. They were in the same order as for the 
3x3 distribution (see Section 3.1.2). The results, when selecting 
a varying number of points in each tie point area, are presented 
in Fig. 3 together with the 3x3 case. It can be concluded that a 
denser distribution had no significant effect on X and Y. An 
effect could though be seen on Z, which was clearly better in 
the 5x5 case if relatively few points were selected in each tie 
point area. When the number of points in each tie point area 
reached 15, Z was practically equal in both cases. 
3.2.3 Reducing the completeness of the observations 
In Section 2, a problem with matching failures and reduced 
completeness was presented. The effect of reducing the 
completeness of the tie point observations was empirically 
tested. Observations selected in Section 3.2.1, were split into 2- 
and 4-neighbouring observations (see Fig. 1) and to pairwise 
observations in all possible combinations. 
The results are presented in Fig. 4, together with the complete 
case. It can be concluded that: 
e The accuracy of the block was decreasing when the 
completeness was reduced, as expected. 
e The accuracy of the case with 4-neighbourhood was 
practically as good as the accuracy of the complete case, 
when a sufficient number of observations (>10) was used in 
each tie point area. 
e The accuracy of the case with pairwise observations in all 
combinations was better than expected. It was only slightly 
worse than the case with complete observations. 
e The case with 2-neighbouring observations was clearly 
worse than the other cases. Especially the RMS errors in Z 
were bad (in the order of 10 cm, not shown in Fig. 4). 
3.2.4 Combining pairwise and multiple matches 
In the system at FGI, when measuring tie points, the goal is to 
make as complete observations as possible (maximal number of 
overlapping images), which is not necessarily an optimal 
approach. This is mainly because the local distribution of tie 
points may get poor in difficult overlap areas. This was tested 
by combining a varying number of multiple matches (selected in 
section 3.2.1) with a varying number of separately performed 
pairwise matches (carried out in the Gruber positions between 
2-neighbouring images). 
When combining all the measured pairwise observations with 
the selected 3 points case, the RMS errors were: X: 20'cm, Y: 
2.4 cm and Z: 3.6 cm. Y was clearly better, and X and Z on the 
same level as for the best cases using only multiple 
observations. 
The results, when combining a different number of pairwise and 
multiple observations are presented in Fig. 5. The following can 
be concluded: 
e Adding observations affected especially cases where only a 
few multiple points (2,3 or 5) were selected. The accuracy 
in these cases was better for X and Y (especially in Y) than 
in cases where 10 or 15 multiple points were selected. 
e Using a large number (10-15) of multiple observations or 
using a few (for instance, 3) multiple observations and 
adding more than 10 pairwise observations, gave about the 
same accuracy in Z. 
341