(15) 
coordinate 
would be 
artometric 
coordinate 
| (15) the 
TM, ie. 
‘ation (13) 
ite side of 
condition 
oint in the 
oelongs to 
same line 
ee (in the 
'e. In this 
nt point in 
composed 
than that 
Xy'. The 
oint in the 
ates are 
(16) 
(18) 
ixel it 
in with the 
(19) 
Lets assume that we are building the image of a 
rectangular terrain area. The domain of the function 
F(X,Y) is a rectangle. The domain of the function F, (x',y") 
is also a rectangle. The set of indices of the pixels P' of 
the image F, and of the pixels P" of the terrain grid is the 
same and can be written as 
IP 4) e (ez? osisi osisig (20) 
If we know the indices of the pixels the coordinates of the 
centre of the pixel P; can be calculated in the coordinate 
system O’X’y’. They will be equal: 
x zd yis Did (21) 
2 j .;2 
According to (10) we have 
(ye ei) (22) 
Building the orthoimage we fill the grid of the pixels P' of 
the side d with corresponding grey levels changing 
successively the indices (20) in the lines and columns. 
Then using the previous associations we can indicate 
possibly precisely from which point in the photo the grey 
value should be taken or which points should be chosen 
to calculate it . 
If we are building the digital othoimage 
G: Pj — Ci (23) 
means that we are building the image in the ground 
coordinate system 
Gy: Pi — Ci (24) 
because | moving along the pixels  P', corresponds to 
moving in the terrain along squares of B sides and 
centres determined by the formulas (16) and (21). 
To determine c; we will compare G, and F images 
assuming thatthe distance between the images should 
be the smallest i.e. 
1 1 
HR 
[Fo v)-G,0,vy?axv- X Y gxv)-o? -min (25) 
D. i=0j=0p" 
lj 
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It results that 
ff (FO, Y)dxv - B^c =0 (26) 
ij 
The pixel P', of the orthoimage should then obtain the 
grey level 
gs INT [[F(X,Y) dXY) (27) 
B^p* 
j 
ij 
During the orthoimage generation the values of finite 
sums 
  
  
| k 
e ANT ert i02 ROC Y 
) (21+1)(2k+1)n=-Im=-k. ^! 242 ! 2k+2 
(28) 
are calculated more quickly than the integrals (28). 
For k=I=0 it is obtained 
0j =F(<;,Y;) (29) 
and then the orthoimage is the function 
(ij) 9 F(F4te (1.1) (30) 
The reconstruction (resampling) of the image by the 
averaging formula (29) causes that each average 
decrease the variance what can be observed as the 
smearing of the contours details. On the other hand 
using an interpolation by the duplication (30) we obtain 
the image more distant from the original (scanned 
photograph). 
3 Construction of DTM 
In the previous paragraph it was assumed that for the 
given area the function Z-H(X,Y) is known, i.e. the digital 
terrain model (DTM). 
This model could be prior determined and written in an 
appropriate data base. If DTM doesn’t exist then it can 
be obtained by one of the following ways: 
e digitalization of the contours of the existing maps, 
e the direct terrain measurement, 
e the photogrammetric methods from at least two air 
photos (stereo pairs).