ISPRS Commission II, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002 
  
AZ IMAGE SYSTEM 
    
  
214 
- 
Y p P 
A p 
uu P ON 
/ / / 
7 x / A v y 
pl 
BACKWARD NADIR 
Ff Hi 
e 
FORWARD 
Figure 3. Geometry of simulated one-lens three-line 
sensors. 
500 — = 
400 — 
300 
Z Axis 
200 8.2 
| e Let 
100 a? * supr 
| 9 © ll C so 
EON rA ur 1 
X Axis 
Y Axis 
Figure 4. Simulated aircraft trajectory, together with 
GCPs. 
200} «80 65.60 455 90 uo 68: +65 
| 09 uu «0 
100} 55 
Pr ius „65:60 urbe, E A busco MA 2 
| 50 — 
-100 - 62 
-200L «59 +60 70 
a i 457 i455. wo i #65 | i 73 i o77 
-1000 -800 -600 -400 -200 0 200 400 600 800 1000 
X Axis 
Figure 5. Distribution of simulated 40 GCPs, with 
their heights, in meters. The aircraft trajectory is also 
represented. 
Y Axis 
60-465 071370 
41 Back projection 
The aim of back projection is to estimate the pixel coordinates 
(u= row number, v= column number) of the GCPs, using their 
known ground coordinates and the known external orientation 
for each sensor exposure. 
The u coordinates can be determined from the well-known 
affine transformation between pixel and image coordinates: 
Ne 
"I5 p (17) 
where n, is the number of pixels per line and p, the pixel size in 
y direction 
Solving with respect to u and setting n,=10200, it yields to: 
A - 250 
us 51004 (18) 
Py 
As far as v coordinate is concerned, it must be found at which 
time (or in correspondence of which image line) the ground 
point is observed by each CCD array. The first step is to 
calculate the image coordinates with Equation 2, using as 
external orientation the data corresponding to the first 
exposure. The computed image coordinates refer to a local 
system centred in the lens PC, with x-axis tangent to the flight 
trajectory, y-axis directed along the scanning direction and z- 
axis upwards directed. Then the calculated x- coordinate is 
compared to the theoretical one, called x,, which is defined in 
the following way. According to the one-lens sensors geometry 
shown in Figure 3 and assuming that the linear CCD arrays are 
perpendicular to the flight direction and no distortions nor 
relative movements occur, x, is constant for all CCD elements 
belonging to the same line (F=forward, N=nadir, B=backward) 
and is equal to: 
XcF - f tan(ay ) 
Xen = ftan(ay) (19) 
Xe = ftan(opg) 
where og np are the viewing angles and x,z, x,y and x,, the 
theoretical x coordinates for the forward, nadir and backward 
viewing lines. As , 0s;70, x, results equal to 0. 
If the difference between calculated and theoretical x- 
coordinates is bigger than the threshold of half the pixel size, 
the image coordinates are recomputed using the external 
orientation corresponding to the next exposure. 
The procedure continues until the difference between calculated 
and theoretical x coordinates is smaller than the threshold. The 
corresponding exposure number will be then taken as v 
coordinate. The algorithm is applied to each GCPs for the 
forward, nadir and backward directions. As result, the GCPs 
image coordinates in the three images are obtained. 
S. TEST ON SIMULATED DATA 
In order to test the indirect georeferencing model, some 
perturbations in the known sensor external orientation (Xe, Ye, 
Zo, Wc, Qc, Kc) were introduced and afterwards estimated using 
the indirect georeferencing algorithm. The perturbed position 
and attitude (X ^, Y'c, Z'c, 0' c, 9' c, K' c) are defined for each 
exposure / (/ - 1,...,A/) as: 
Xc2Xc AX Ay sin(nz-1/ AL) 
Yc =Yc +AY + A, sin(n-x-1/ AI) 
Zc=Zç+AZ+4; sin(n-x-1/ AI) 
Qc — Gc AQ A, sin(n-z-1/ AI) 
c 796 *^9*4, sin(n-z-1/ Al) 
Kc 9 Kc AKA A, sin(nr-1/ AI) 
where n is the number of cycles and A/ is the number of 
exposures. In the test, A/= 40832, AX= AZ=2.0 m, AY-1.0 m, 
Aw=0.2°, Ag- Ax-0.3?, AX-AY-AZ-0.3m, Ae Aq- AK-0.1? 
and n=5.