Plate system 
Ground 
System 
Figure 3 : Diagram of the DLT Principle. 
x+(x-x )rk +(r +2(x-x,) )p, + 
LX+E V+EZ+E 3) 
TXy- X—X = 
(y, X JP; LX+L Y+L Z+1 
yt(y-y,)k t. €Xy-y,) Jp. * 
2 X LX+L Y+L Z+L 
+ = X—X m5 sta pm mA RUE 
( Yo p, L'X+L Y+L Z+1 
with r 7 (x^ry?)'? 
where: 
e X and Y are the co-ordinates comparator of the image 
points. 
. xo and y, define the position of the center of the plate in the 
comparator system. 
X -Y 7]. 0g 0 0 0 x 
0 0 0.0 -X.:Y -Z =I vx 
Each object point known in ground co-ordinates lends itself to 
two similar equations. A minimum of seven points is necessary 
to solve the problem correctly, but to have a good determination 
of the unknown parameters of the transformation, the number of 
fulcrums must be higher than that which would be necessary, 
which leads us to a resolution by the method of the least- 
squares. It is worth pointing out that it is possible to use this 
method together with the two conditions (colinearity and 
coplanarity) for a more refined treatment [6]. 
2-4 Adjustment of blocks 
In this type of work, one cannot genuinely speak of block 
compensation, since the nature of the object is different from its 
geographic space. However, there is a great similarity with the 
aero triangulation considering the principle of the functional 
model used, namely the beams method. In this situation where 
one is concerned with in an exact definition of the object, the 
total compensation principle (block adjustment) is based on an 
installation through DLT calculation and a final compensation 
using the external parameters. The observation relations used 
must take into account all the perspectives representing the 
subject. 
Each beam gives place to fourteen parameters and each object- 
point known gives two equations. It is thus possible to pose an 
observation relations system between co-ordinates, parameters 
and distances. 
The compensation principle is based on the rigorous method [7] 
which deals with the adjustment of the plate observations. 
*  K, ,p; and p, are the parameters of distortion of the 
objective; 
e  X,Y, Z are the ground co-ordinates of the points 
photographed 
e  L,through L,, are the unknown coefficients of the beam. 
The following expressions can be deduced directly from the 
system (3): 
L,X + L,Y + L32 + L, - xAL, — XYL,0 -xZL,, — 
-xr Ak sit +2x )Ap, -2VKAp ~X=1 
LX LY #1. Z+ Lr yXL, =yYL y= Y71= 
2 2 2 4 
er Ak —(r 2x )JAD, -2yxAp —y-r « 
where : 
e A=L9X + LuY+LuZt+I1 
®  r,andr, y are residue errors in condition equations. 
e IL, .., Lj are parameters drawn from spatial 
transformation (scale factor, rotations and translations). 
They are considered independent as far as DLT is 
concerned. 
e  L;,, L,3, Ly4 are the distortion coefficients of the objective. 
with Ak,=K", =L;2, Ap,=P'=L;3, Ap,=P'7=L;4 ; the system of 
equations (4) can be reduced to the following matrix form : 
xZ x (r +2x ) 2yx ZI I 
YY V7 quac ya ac (ey) pe: I 
3 - Treatment Processes 
3.1 Preliminary treatments 
These treatments include: 
- The orientation of the photographies : (x,y) = R(x’,y’) with 
[] rotation matrix of the photography which is written as : 
x! cosa —sin a || X 
8l : (5) 
y sina cosa || y 
- The observation treatment : 
The observations in space image of the plate co-ordinates are 
sullied with errors in dots since measurements are done 
separately (non stereoscopic dots). In this case, it is necessary to 
check the reliability of the observations by taking into account 
the parallax equations (6). 
PL. =x; —X; i=l+n (6) 
The calculation reference is based on the following parameters: 
*  H, H, distance between i and the reference (0), figure (4). 
e PL longitudinal linear parallax of the point of reference. 
e AH, =H, — H,, difference in distance. 
e AP], difference in parallaxes between the reference and 
point I. 
—112— 
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