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Table 2. 
The deviations VxVy of 16 czosses in the 1-st and 
4-th quarter of the photograph which result from the 
bilinear transformation made on 4 active crosses 
placed in the corners of each quartez. 
  
  
  
  
  
  
  
  
  
  
  
Names of surveyed photographs 
,) | LA DP2| DPa| sa]. esa| 124| L2 | 14 | P2 | P4 | s2.| 217215 
— [4m] } [m] 
1-st quarter — Vx [4m] 
111 0.0| 0.0| 0.0| 0O.0| O.0| 0O.0| 0.0| 0.0| 0.0 0.0| 0.0| 0.0j O.0| 0.0 
121-2.4|-0.4|-3.8] -1.3! 0.9|-2.6|-2.1|-1.0 -1.0| 0.6j| 1.3|-1.4|-1.2;:i.4 
131-0.6|-1.6|—4.8| 1.5| 0.0, 0.8/-0.5|-0.5|-2.5|-0.7 1.2]-0.11-0.7!xz1.6 
14| 0.0| 0.0] 0.0| 0.0| 0.0| 0.0j 0.0/.0.0| 0.0|. 0.0 0.0| 0.0] 0.0j. 0.0 
21] 0.7| 0.7| 0.0|-2.0| 3.2| 3.2| 2.9| 0.8| 0.6, 2.1| 0.5 1.3f 1.2/1.4 
22|1-31.3] 0.9|-1.5|-0.7| 3.2| 2.9|-2.6|-1.0| 0.0| 1.5 1.8] 0.9] 0.31£1.7 
23|-0.2|-0.1|-0.6| 1.4|-0.1| 1.0| 0.3; 0.1|-2.4|-2.0 -2.5|-2.1]-0.6|£1.3 
24|-0.9|-3.0|-1.5| 0.7| 1.9] 2.5]-0.6|-1.0|-3.1|-2.4 -1.4|-1.8|-0.9| £i.7 
al 1.1| 2.6|-2.8|-2.3| 2.8|]-1.6| 3.7| 1.1| 3.0| 0.5: -1.8| 1.1 0.6] t£2.1 
32|-0.4| 0.1|-3.2|-1.7| 2.5| 2.5| 4.5| 0.2| 2.2] 3.4|-0.5 -0.8| 0.7|x2.2 
33| 0.9| 0.1|-1.0|-0.3) 0.0| 2.9| 2.7|-0.3| 0.1|-0.3|-2.0,|-0.2 0.2|z1.3 
24| 0.9|-0.2|-1.0|-31.3]-0.8| 1.1|-2.7|-1.4|-1.2|-1.7| 1.3 1.1/-0.5/=1.2 
41] 0.0| 0.0| 0.0| 0.0| 0.0, 0.0, 0.0| 0.0| 0.0| 0.0| 0.0| 0.0 0.0| 0.0 
4211.4]. 1.4] 1.2]-0.4l] 0.0]. 2.2]-0.8|-0.1]-1.0]-1.6 -0.6|—-1.01-0.2| £1.1 
43! 2.9] 1.2|-1.4| 0.9} 1.0] 0.6! 1.6|-0.8| 0.0|-2.3|-0.5 -0.5| 0.2/#1.4 
44| O0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0] 0.0| 0.0| 0.0| 0.0 0.0| 0.0 
1-st quarter — Vy [um] 
11ll o0.0| 0.0] 0.0] 0.0] 0.0| 0.0f 0.0] 0.0f 0.0{ 0.0| 0.0 0.0 0.0] 0.0 
12] 0.8|-0.8| 2.1|-0.3| 4.2|-1.0| 1.4) 0.1|-0.2|-3.1] 1.4 1.0} 0.5} =1.7 
13/-2.2|-1.0|-1.6| 1.1| 0.0|-1.6|-1.7|-0.9| 4.6|-4.7| 0.1|-1.9/-0.8 £2.1 
34| 0.0| 0.0| 0.0] 0.0] 0.0] 0.0] 0.0] 0.0f 0.0f{ 0.0| 0.0{ 0.0} 0.0 0.0 
211-3.3|-2.61-0.6|-3.6| 0.3|-2.8|-3.1|-2.5|-1.6|-7.6| 0.9|]-2.1 —2.4/|+2.1 
22/-0.1/-1.2|-2.1|-3.4|-0.8|-2.0|-2.6| 3.2|-1.9|-10.} 1.7|-2.8 -1.8|z3.1 
23|-1.6| 0.01-0.8| 0.2|-0.7|-2.1|-1.3| 3.4| 0.8|-6.3| 1.0|—4.8 -1.01z2.5 
24| 1.9|-1.6|-0.4| 1.0|-0.7|-6.0| 0.7| 2.2| 2.0|-5.5| 3.5|-0.7 -0.3|£2.8 
31| 0.5| 0.3| 0.3!1.7/|-1.8|31.8|-0.5|-0.9|.1.8|-4.4| 2.3| 0.3/-0.5 *1.7 
32| 1.0! 1.1|-0.4|-2.5|-1.8| -.0|-2.0| 0.9| 0.7|-5.4| 3.6|-0.2/-0.5 t2.2 
33|-31.0! 0.6|-1.8| 1.7| 1.2|-2.5|-0.2]-1.0| 1.0|-2.2| 0.8|-1.7]-0.4 =1.4 
3a| 0.3| 0.5| 0.1| 4.3| 0.5|-2.7| 2.5| 2.4| 3.1/—1.2| 1.3|-—2.3/ 0.7 t2.0 
41| 0.0| 0.0| 0.0| 0.0! 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| O.O| 0.0 0.0 
421-0.7|-1.6| 0.4|-1.5|-0.5|-0.9|-0.2|-0.2| -3.0|-2.4| 1.8|-2.4 -0.9|£1.3 
43l-2.81-0.4| 0.7|-0.4|-0.3/-0.5|-1.0|-2.4| 0.7| 0.0| 2.1,-1.5|-0.5 +i.5 
44ll 0.0| 0.0| 0.0| 0.0] 0.0| 0.0| 0.0} 0.0] 0.0| 0.0} 0.0] 0.0 0.0| 0.0 
4-th quarter — Vx [um] 
A1l 0.0] 0.0] 0.0] 0.0] 0.0] 0.0] 0.0] 0.0| 0.0] 0.0] 0.0| 0.0} 0.0 0.0 
42|-1.3] 1.4l| 1.21-0.4| 0.0| 2.3|-0.9|-0.1|-1.0|-1.6|-0.6|-1.0 -0.2]z1.2 
43/ 3.0| 1.2|-1.4| 0.7! 0.9| 0.6| 1.4|-0.8| 0.0|-2.3|-0.6|-0.5 0.2{x1.4 
aa 0.0] o.ol 0.0] 0.0] 0.0] 0.0} 0.0] 0.0] 0.0] 0.0{ 0.0] 0.0} 0.0} 0.0 
sill 0.6! 4.9! 3.4] 1.1] 4.8] 6.3] 4.5] 2.1] 6.2] 3.1] 2.5] 2.9} 3.5{%1 8 
s2 0.71 4.2] 1.0] 2.2] 4.7] 2.6] 1.9] 2.0] 4.9] 4.2{ 4.1 1.4) 2.8/1 4 
53| 0.9| 2.9| 2.5] 3.7/-0.6] 1.1| 3.1] 0.0| 1.4|-3.0[-1.1] 1.0f 1.0[*1.9 
54| 0.5| 0.3|-0.5| 4.7|-2.2|-2.7| 3.0| 1.5| 1.4|-1.2| 1.8| 3.2 0.8] £t2.1 
614 0.11-0.1] 6.1] 2.5] 5.9] 4.0] 4.0] 5.6] 6.3] 3.1{ 2.8] 4.7] 3.8 z2.1 
62] 3.31 1.1] 5.0] 4.9] 5.4) 3.1] 5.6] 2.9] 4.5] 2.7] 2.6] 2.6] 4.1 £1.7 
63| 1.4| 4.0| 3.6] 4.5|-1.0| 2.9! 5.1| 2.0| 4.0|-0.5| 1.7| 2.8j 2.5 t1.8 
64|-0.711.3! 1.0] 1.1/-3.5|-0.4|-31.7| 0.0| 3.3|-0.9| 2.2/-0.1|-0.1 ti.7 
71| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0:0, 0.0; 0.0] 0.0| 0.0 
72| 4.11-.8| 0.8! 31.6]-1.1|]-1.8] 1.5| 0.6| 1.6| 5.0] 2.0| 2.4] 1.0 z2.2 
73| 3.6| 1.2] 1.01 3.7] 7.5]-1.8| 1.4| 0.9] 2.9] 1.1] 3.6| 2.8] 2.3 42.2 
74| 0.0] 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0{ 0.0{ 0.0} 0.0 0.0 
4-th quarter — Vx [4m] 
41| 0.0] 0.0| 0.0] 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0] 0.0] 0.0 
421|-0.7| 1.6! 0.4|-1.6|-0.6| -0.9|-0.3|-0.2|-3.0|-2.4| 1.8|-2.4|-1.0|t1.3 
43|-2.8|-0.4| 0.7/-0.4|-0.4|-0.5|31.0|-2.4| 0.7| 0.0| 2.1|-1.5|-0.5, 21.3 
4A| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0] 0.0| 0.0 
51| 5.8| 6.6| 4.8! 4.5| 4.2| 5.9| 6.3| 4.8| 7.8| 4.2! 4.3| 6.5] 5.5|£1.1 
52| 7.1) 2.1| 2.5| 3.5| 3.3| 4.2| 3.4| 4.4| 6.2| 3.3| 2.0| 3.8| 3.8|t1.5 
53| 1.8| 0.5| 2.0| 4.9] 3.0| 1.1| 4.0| 2.3| 2.7|-0.1| 4.3] 1.0} 2.3|%1.5 
5a|| 1.3/|-1.0| 2.6| 3.3| 0.7] 2.0] 1.2{-1.2| 2.3|-1.1| 1.0] 0.3} 1.0/#1.4 
61ll-0.5| 4.1| 6.5] 7.7| 5.2| 2.5] 6.9] 7.5| 9.0] 3.8] 5.0] 6.4} 5.3|£2.5 
62| 5.5| 6.5| 5.1| 5.0| 5.8| 4.9| 6.6| 6.7| 5.5| 6.7| 8.4| 6.1| 6.1|t1.0 
63| 4.2] 7.2] 3.1] 1.9] 3.1] 4.5| 5.2] 2.9| 5.6] 2.6] 5.2| 4.9] 4.2/+1.4 
64|-0.1| 2.2| 4.4| 3.0! 0.4| 4.2| 5.7| 1.3| 4.3| 0.5| 4.7|-1.2}| 2.5{*2.1 
71| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.01 0.0| 0.0 
72| 1.7| 0.1|-0.7|-0.1|-3.9|-0.9| 2.3| 1.7|-0.6| 2.6/-1.8|-1.6]-0.1]|£1.8 
73| 2.4|-2.0| 0.6|-0.7|-3.1| 0.0|-0.7|-0.7| 0.4| 1.0| 1.6] 1.9] 0.1,t1.5 
74| 0.0| 0.0| 0.0! 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0| 0.0 0.0| 0.0 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
1) reseau cross number 
2) average deviation for each reseau cross 
3) mean error of the average deviation (o) 
It must be considered, however, that - as it is shown 
in the table 2 - the coordinates after bilinear trans- 
formation do not always deviate very regularly (eg.P4- 
Vy-22). Therefore, sometimes the correction of 
coordinates by the interpolated mean systematic 
residual value can rather deteriorate than to improve 
the accuracy. It would be advisable in our case, 
therefore, to neglect such corrections for the I-III 
quarters of the image, considering the fact that the 
value of the mean error of the average deviation 
are close to the eveztual correction. So, only sys- 
tematic corrections to the coordinates after bilinear 
transformation wouid be applied to the IV quarter 
and partiall to III quarter (see fig.4 and table 2). 
Nevertheless, for the top accuracy projects where 
single microns are of the great importance, there 
would not be enough to measure only 9 active 
crosses in each reseau frame. In such cases which 
require the top accuracy the image coordinates must 
be transformed individually in each little quadrangle 
formed by crosses around the image surveyed point. 
Sometimes the correction procedure could require 
the measurement of all the 49 reseau crosses. 
42. Calibration of the semimetric reseau camera 
The camera was calibrated using pictures of the 
special flat test-field. It is 2:28x228 m grid of 
squares consisting of 161 targets and 40 additional 
targets placed to thicken control points on the 4 
symmetry axes. The test-field was enriched with 5 
control points placed in the space in front of the 
flat test grid. The spatial coordinates of the test 
field were determinated with the accuracy +0,2mm 
applying mixed direct and photogrammetric methods. 
There were taken 2 triplets of photographs so 
oriented to secure the best possible geometry cross- 
ing of the projection rays (2 photographs were taken 
from left and right site from the for level, and the 
third was taken frontally, but from just under the 
ceiling). Both triplets were taken using Biometar 
2.8/80, one within the distance of 2 m, the other 
within the distance of 4m from the flat grid test. 
The calibration calculations made with the use of 
bundle adjustment program (by A.Tokarczyk, AGH) 
gave excellent accuracy of 0.1+0.3 mm on the 9 
control points (5 on the flat test-grid and other 4 in 
the space in front of the flat test) anc provided the 
interior and exterior orientation clements. For 
D=2 m we received Ci =87.79+0.018 mm, Xo =-0.08 
+0.020 mm, ÿo = -0.52+0.023 mm, mo = +0.0033 mm. 
For distance D=4 m the following elements were 
evaluated: Cr=85.64+0.009 mm, xo=0.01+0.008 
mm, yo = -0.49+0.008mm, Mo = +0.0014mm. The cal- 
culations in both cases were performed under con- 
dition that the interior orientation elements are 
stable for pictures of the triplet. All the targets of 
the test field were used to calculate distortion of 
the camera objective. The radial distortion of the 
reseau pictures (recorded on film) compared with 
the distortion of the camera before adaptation (pic- 
tures recorded on the glass plate) changed very 
little due to the additional glass-plate within the 
camera optical system (see fig.5). The maximal radial 
distortion is greater by 10% on the picture taken 
with the reseau glass in comparison with picture 
taken with non adapted camera.