The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
measured with sub pixel accuracy by using centroiding method. 
Then target points were matched using epipolar plane angle 
method which was proposed by Sabel (1999). 
8 B «_ 
m o o 
mm 0 
o ** it m 
a m 
* * 
0 D 
** o a 
m-r 
a 
if 
Q 
. 
» _ 
a 
* B t g 8 
i * m 
0 
m 
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Figure 1. Test field 
After these procedures were completed, the monitoring stage of 
signalized target points on test material under load can be begun. 
The entire process is composed of three steps. 
• After Each load application, acquisition of the multi 
image sets of test material, 
• the measurement of image coordinates of target 
images which was matched in previous steps, 
• The computation of the 3-D coordinates of these 
points by forward ray intersection using the results of 
the calibration process 
• 
An algorithm similar to the method which proposed by Maas 
was used in order to remove the refraction effect. In loading 
tests, test field was placed as parallel to transparent Plexiglas 
which was used in front of the test box. The principles of 
algorithm are shown in Figure 2. If the point P (X, Y, Z) in 
object space is shifted to P (X, Y, Z), the collinearity condition 
can be applied for P using the object coordinates of the shifted 
point P. 
Figure 2. Radial shift for compensation 
Only a radial shift by AR parallel to the XY plane has to be 
computed for each point relative to the nadir point of each 
camera (Maas, 1995). 
From figure 2 can be derived: 
F 0 tan /?, +1. tan /? 2 + Y p tan /?,=/? 
(F 0 +1 + Y p ) tan J3 X = R 
With Snell’s Law 
n x sin /?, = n 2 sin ß2 
(3) 
the system describing the multimedia geometry is complete. 
Equations (1), (2) and (3) can only be solved iteratively due to 
the trigonometric functions. If P is chosen as a first 
approximation for P and 
R m = ) 2 +(z„-z 0 ) : 
(4) 
the angle of incidence in the medium nl in the first iteration 
becomes 
/?, = tan 
l (0) 
V^o +/ + y p j 
(5) 
The angle of incidence in the plexiglas media according to 
Snell’s Law and the correction for R<o) are computed by using 
following equations. 
ß 2 = sin 1 sin /?, j 
(6) 
AR _ ( sin (A - ßi ) 
cos /?, cos ß2 
(7) 
R — R(Q} + A R 
(8) 
The equations (5)-(9) are used iteratively until the difference 
between consecutive AR values are equal or smaller than the 
predefined threshold value (0.001 mm). And finally the 
coordinates of the radially shifted point is computed. 
X p =X 0 +(X p -X 0 )R/R 
l p =Z 0 +(Z p -Z 0 )R/R 
The collinearity condition for cameras Cj can then be used with 
the radially shifted point Pj (X, Y, Z) instead of P (X, Y, Z) 
(Maas, 1995). 
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