—— 
—M M — es 
~~ ls 
Table 1. 
Bilinear transformation in the reseau frame quarters 
for 16 active crosses or 4 active crosses (only in the 
corners of each quarter). 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
BILINEAR TRANSFORMATION 
Name| N° 16 active crosses 4 active crosses 
of | of {standard deviation for Stange go Tite for 
16 active crosses SVOSSES passive 
photo| film = 
m m m m m m 
x y P x y 
[m] [pm] [ini [m] [m] [pm] 
The first quarter of photograph 
DPp2 | III 0.9 0.9 1.3 1:2 1.9 1.6 
G52 | IIT 1.0 1.4 1.7 1-1 1.9 2.3 
DLA | III 1.0 1.3 1:7 1.2 1:5 1.9 
DP4 | III 1.5 1.0 1.8 2-0 1.0 2.3 
GS4 | III 1.1 1.2 1.7 1.6 1.3 2.41 
12 II 1.9 1.3 2.5 2.1 1.5 2:6 
P2 II 1:2 1.6 2.0 1.6 1.9 2.4 
S2 II 1.1 1.1 1.6 1.2 1.7 2.1 
IA II 0.6 1.6 1.7 0.7 1-7 1.9 
PA II 1.3 2:6 3:0 1.6 4.5 4.8 
S4 II 0.9 1.4 1.7 1.0 1.9 2.2 
L24 I 1.6 1.4 2-1 1.9 2.2 2.9 
im 1.2 1.4 1.9 1.4 1.8 2.4 
o £o0o.3|t-t0.4l] 0.4] £0.41 * 0.9] £t 0.8 
The second quarter of photograph 
DP2 | III 1.0 1.2 1.5 i.0 1°3 16 
GS2 | III 1.5 1.6 2.2 2.2 2.3 3.1 
DP4 | III 1:5 1.3 1.9 2:5 1.4 2.9 
GS4 | III 1.0 1.9 2.0 1:3 1.8 2.2 
I2 II 1.5 1.2 2.0 1.6 1.6 2.3 
P2 II 1.5 1.3 2.0 2.1 1.6 2.6 
S2 II 1.9 2.7 3.3 2.9 3.1 4.2 
P4 II 1.8 2.7 3.2 2.5 3.6 4.3 
S4 II 1.8 1.6 2.4 3.0 2.5 3-8 
P24 I 1.6 2.4 2.9 2.1 2.5 3.3 
nl 1.5 8 2. 2.1 2.2 3.0 
o +.0.3 * 0.6 £ 0:6 +:0.6 0.7 = 0-8 
The third quarter of photograph 
DP2 | III 0.9 1.4 1.7 1.4 1.6 2.1 
652 | 111 1.6 1.3 2.0 2.2 1.5 2.6 
DP4 | III 0.9 1.6 1.9 1.2 1.8 2.2 
GS4 | III 1.0 1:7 2.0 1.4 2.4 2.8 
L2 II 1.3 1.6 2.0 1.6 2.2 2.7 
P2 II 1.2 1.5 1.9 1.5 1.8 2.3 
S2 II 1.4 1.7 2.2 1.8 2.4 3.0 
PA IT 0.8 0.9 1.2 1.0 0.9 1.4 
SA I 1.2 0.9 1.6 1-5 1-1 1.9 
Er 1.1 14 | 18 | 1.5 1.2 | 2.3 
o $0.3 } + 60.35} + 0.3} : 0.3} £t 0.5] t 90.5 
The fourth quarter of photograph 
DP2.| III 1.8 2.7 3.2 2.2 3.3 4.0 
GS2 | (IL 1.9 2.5 3.2 2.6 3.2 4.2 
DLA | III 1.4 2.5 2.9 1.9 3.1 3.6 
DP4 | III 1-7 2.1 2.7 2-5 2.9 3.9 
GS4 | III 2.7 2.6 3.8 3.4 2.9 4.5 
12 II 2.0 2.6 3.3 2.8 3.7 4.7 
P2 II 2.1 3.2 3.8 3.2 4.2 5.3 
S2 II 1.4 2.6 2.9 2.1 3.6 4.1 
LA IT 1.3 2.3 2.6 1.9 3.3 3.7 
PA II 2-2 1.8 2.8 2.9 2.6 4.0 
S4 II 1.4 2.6 3.0 2.2 9.3 4.0 
124 I 1.9 2-2 2.9 2.5 2.9 3.8 
imi 1.8 25.4 3.1 2.5 53.1 4.2 
c £0.4] to0.3]-0.4] £0.5] € 09.4 :£ 0.5 
  
  
  
  
  
  
  
  
  
For all the 12 passive crosses in a guarter which 
were not used as the control-points the residuals 
were calculated and analyzed together with the four 
v = 0 which were obtained on active crosses. The 
following average standard deviations for each 
quarter were achieved: 
— for the I quarter avr.mp=2.4ur1, o= =0.8um 
— for the II quarter avr.mp = 3.067, o= =0.8um 
— for the III quarter avr.mp = +2.3ux, o= X0.5um 
— for the IV quarter avr.mp = +4.2p52, 9 — x0.5um. 
The average standard deviation for the zu reseau frame 
in such case of calculations amounts ia =3.0um, what 
would be satisfactory for many applications. The 
differences of accuracy which are shown in above 
quoted average mean errors were calculated from 
individual deviations of each measured reseau cross. 
The values of individual deviations Vx, Vy are shown 
in the table 2 for the best and thc worth quarter 
of the pictures (quarter I and quarter IV). The 
average deviations (bilinear transformation on 4 ac- 
tive crosses) for each quarter of thc reseau frame 
are shown on fig.4. 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
1 
11h À IET A ka 114 14, ! 4 7117 
1 1 7 
\ \ \ / i | / nl 
| / 
A i i 
\ ! / : / / 
ie quu. A m T. 7 
Ve o —----7 1 ! i AZ) ne À i 
e] \ i i TR \ \ 
! \ 1 \ \ \ 
! i \ i | * \ \ 
\ | \ \ 
! : 1 i \ N Y 
i | ! 1 \ \ \ 
1 | ! | X \ \ 
I i = \ \ 
; b — go = = À \ 
mama es me ee rr | NR mle tL U 1 
! I l | ' | Y E 
! ! | | 1 1 \ 1 
! 1 ! ! 1 1 \ 
1 | 1 ! ' 1 \ \ 
I i | | I ! \ \ 
, 125 diet | 2-nd t \ i 
I ; quarter quarter ! 3 i 
4 | hy a mer en = dl] 
—— à b 
Se a ep (AA i 17 
\ 
N \ 4-th i 1: 3-k | | 
DIS NS | quarter t | quarter | | 
Te E | = 
oe \ \ 
! \ scd \ \ | | i 
i \ E. \ \ I I ! 
' \ \ Sa ep] Yan an mmm mlm om mn we fe [777A 
+ i I | 
| Y x I | | : 
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-—-7--— \ 1 | 
+- A | ! 
4 7 F--X i i | ' i 
A Z SR | | , i 
/ | € ! I | i 
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7 / I Be ae aw he we ve] a! 
L i I 
4 1 I T 1 
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ny / | TL 74 \ ! 177 
RN | = 
seen e t 
d C 
Fig.4 a,b,c,d. The average deviations of coordinates 
of each reseau cross, calculated using bilinear trans- 
formation with 4 active crosses in scparate reseau 
frame quarters. 
It is noticeable, that biggest deviations appear close 
to the limits of the frame (fig.4). The average values 
of Vx or Vy fixed for certain reseau cross (the mean 
systematic residuals) could be used as the systematic 
corrections to improve the accuracy of determination 
of image coordinates.