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Assuming that only the image coordinates 
X, Yy X3. Y, affect the accuracy, one 
can use the well known simplified for- 
mulae for the calculation of the expected 
accuracy 
Zz 
m,-m.---m 
X Y cx 
222 2Z 
In, ——— m. = rums 
3 Bc * S(1-p) x 
The accuracies in the three directions 
(X,Y,Z) using the above formulae present 
a linear variation proportional to the 
object distance (Y), if it ise. assumed 
that the Y/B ratio is kept constant (B - 
base). For terrestrial applications and 
assuming that we use contact prints from 
a 24X36 mm format amateur camera with a 
50mm lens and given that the image 
coordinates accuracy is 50 um we get the 
following for the mx, my, mZ (table 1) 
in steps of 5 m. The use of enlargements 
(x5) of the same photos can give a cor- 
responding improvement to the accuracy 
(table 1). 
CONTACTS ENLARGEMENTS 
Y mX,mY mz mX,mY mz 
(m) (mm) (mm) (mm) (mm) 
5 7 35 7 
10 14 69 14 
15 21 104 21 
20 28 139 28 
25 35 174 35 
30 42 208 42 
35 49 243 49 
40 56 278 56 
45 63 313 63 
50 69 347 69 
  
Table 1 
3. EVALUATION OF THE OVERALL SYSTEM ACCU- 
RACY 
The achieved overall accuracy was tested 
in two steps : the first for the written 
software and the second for the system 
(hardware+software). A simulated test 
field with 49 (7x7) points was used. The 
simulated data includes all distortions 
(radial, tangential, shrinkage) and it 
also takes into account the accuracy for 
both image and ground coordinates. The 
orientation of the simulated stereopair 
was calculated with 25 control points 
from the 49, while the other 24 were used 
as check points. The test was performed 
for many configurations of depth of 
field. It was found that the method is 
reliable with a ratio dz/z, (for depth of 
field to distance to object), greater 
  
than 1/100 and it gives results simi- 
lar to the expected. 
In order to compare the obtained results 
to the expected accuracy the following 
discrepancies where formed 
dXx-x-X!' dY-Y-Y! dz-z-z! 
where X,Y,Z and -X',Y',Z' sre the correct 
and the ground calculated coordinates of 
the check points respectively. In addi- 
tion the mean square error (M.S.E.) of 
the differences for every axies was cal- 
culated 
X 2 
(dx)? = (dr)? go 2, (az) 
ext n gy n 2 n 
Table 2 gives the M.S.E. and the maximum 
discrepancies calculated for a configur- 
ation with focal length 250 mm (5x50) 
image format 180x130 (5x(36x24)), Z = 40m 
and dZ = 6 m while the a priori error for 
image and ground coordinates is 0.050 mm 
and 0.01 m respectively. ÀA real stereo- 
pair with similar configuration was used 
in order to simplify the comparison of 
results of simulated and real data. 
The pair was chosen among a total of one 
thousand photos taken for the 
Photogrammetric Survey of the Medieval 
Walls of the City of Rhodos. The original 
negatives of the stereopair were taken 
with à simple CANON amateur camera 
equipped with a 50 mm lens. The photos 
used for the test are 5X enlargements 
(130. X 180 mm). The photos were taken 
from a distance of 40 m. The surface of 
the object presents a depth of field of 6 
m. Figure 1 shows the typical shape of 
the Walls. A” set. of 19 control points 
were observed and determined with geo- 
detic method on the object surfaces. From 
these points a subset of 10 points were 
chosen to serve as control points while 
the rest O9 points where used as check 
points. The respective discrepancies for 
the three axes dX, dY, dZ and the M.S.E. 
where calculated as for the simulated 
pair. The results are shown in table 2. 
CONTROL POINTS CHECK POINTS 
Simulated Model (mm 
14 3 5 
27 11 10 
Real Model (mm) 
35 19 20 
69 41 52 
  
Table 2