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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.