'ABLE OF 
€ exists gross 
in the object 
ted with. The 
tions. It is not 
OSS errors in a 
issumed that at 
The following 
(16) 
sis. 
(17) 
calar. Z, isa 
oss error. The 
sung that there 
vation. 
, the following 
othesis (Koch, 
(18) 
  
J 
. is a co-factor 
a square of 
s the sum of a 
»ss error when 
S à gross error, 
rejected (it is 
fies the testing 
ted for a gross 
vork reliability 
n), it is judged 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
6. EXPERIMENTS 
6.1 Experimental environment 
To examine (1) precision, (2) sensitivity and (3) reliability for a 
typical slope measurement, a slope model of 1,100mm wide and 
S00m high was made. This was about 1/30 scale of a typical 
construction site of a slope along a highway. Figure 2 shows 
one of images exposed in the following experiment displayed 
on the authors’ measurement system named “SUBARU”. 
A total of 34targets of 5 mm in diameter were placed at 200mm 
intervals. This interval is a standard one between anchor bolts 
on road and tunnel slopes. Three points are placed on a board 
at the central part, displacement of which is controllable. The 
other 31 points were stationary. A fixture in the right centre is a 
special device for automatic orientation (Hattori 2002). 
It is usually sufficient if a 2 mm displacement is detected over a 
30 m in width. Thus, the object coordinate precision of 
0.050mm is envisaged to be at least necessary as practical to 
satisfy the other criteria. The experiments were conducted for 
the case of no displacements and for the case where the board 
was shifted by 0.050mm in the Y direction (downward in 
Figure 3). The camera used was a Nikon D100 (3K X 2K 
pixels) with a 20 mm lens. A total of 20 images were taken. 
Four were taken at cach of five stations at a distance of 1,000 
mm, as shown in Figure 1. The four images were taken by 
rotating the camera by 90 degrees around the optical axis. This 
set of images is called Set 20. The set without displacements is 
called Set 20 00, while one with displacements is called Set 
20 50. Similarly the set of 12 images taken at three stations, i.e. 
left, center and right is called Set 12. And the set of eight 
images exposed at two stations, i.e. left and right is called Set 8. 
Magnitude of the displacement is denoted by 00 and 50 in the 
same way. There were no differences in lighting or other 
physical conditions in these sets. 
The most probable values of interior orientation parameters and 
their variance-covariance matrices used through experiments 
are values obtained for simultaneous adjustment of Set 20 00 
and Set 20 50. 
6.2 Precision of coordinate measurements 
The precision (standard deviation) obtained from the adjustment 
calculations for Sets 20 00, 12 00 and 8 00 are shown in Table 
l. The increasing tendency of standard deviation almost 
satisfies the error propagation law. The standard deviation for 
the image coordinates of the targets was about 0.0003 mm. 
However, an empirical value would be about 0.0005 mm even 
under good photo-taking conditions such as exposure, etc., 
based on the authors’ experiences. Thus, it is thought difficult 
to achieve higher precision from the actual measurements. 
Furthermore, an ideal value obtained from the self-calibration 
was used for the prior calibration value of the Camera’s internal 
orientation element. Thus, the results shown below should be 
discounted and regarded to be about two to three times higher. 
However, even so, Set 8 would ensure 1 mm precision at real 
scale. 
  
  
Lynne 500 1000 15.1500 “2000 2500 3000 
firareots  <{ >| target 7 2e] Mod j zum [camera D100, lens 20 mm 
som Of: com of CT Hn Manual] BEBE DU | 3/0] 
ER Lx [:9] 1 J[99 [22 esectif Kouhoi Zentrod Zenpod. d [ exce 
XoYo.2z0| -535.-140. 
  
  
Figure 2. Model a slope displayed on a screen of the 
measurement system "SUBARU" 
Table 1. Measurement precision of object coordinates for 
three exposure configurations 
  
  
  
  
  
  
  
  
  
Set 20 00 Set12 00 Set 8 00 
X (mm) 0.0050 0.0006 0.0078 
Y (mm) 0.0048 0.0058 0.0072 
Z (mm) 0.0148 0.0163 0.0179 
Average (mm) 0.0095 0.0106 0.0120 
  
Table 2. Measurement movement of the three points 
(Set20 00 and Set20. 50) 
  
  
  
  
  
  
  
  
101 102 103 
X (mm) -0.0054 -0.0080 -0.0019 
Y (mm) 0.0340 0.0438 0.0353 
Z (mm) 0.0042 0.0053 0.0127 
  
Table 3. F-test for displacement monitoring 
(Set 8 00- Set 8. 50) 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Z T, (9574) Sy ô for T (20%) 
101 8.93 2.61 2.29 3.3 
101.102 10.08 2.10 3.18 37 
101,102,103 6.04 1.89 2.45 4.0 
(Set 12. 00- Set 12. 50) 
T T, (9596) À ô for n (20%) 
101 8.93 2.61 2.99 3.3 
101,102 10.08 2.10 3.18 3.7 
101,102,103 9.54 1.89 3.09 4.0 
(Set 20. 00- Set 20. 50) 
T T, (9594) So ô for T, (20%) 
101 13.1 2.61 3.62 3.3 
101,102 16.4 2.10 4.05 3.7 
101,102,103 | 14.7 1.89 3.84 4.0