International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B1. Istanbul 2004 
  
convergent lines and the main vanishing point is 7, 
» 
X 
M * UE 
Fig.2: Layoutof3 cameras  Fig.3: Parallel lines? image in 3 
> J o > 
cameras 
2). Image conversion in 3-camera system 
Generally, the three images can be transformed into the 
horizontal equivalent image À through the algorithm given 
below. The transformation principle is illustrated in Fig. 4, 
where 3 cameras’ projecting centers are virtually overlapped 
into one point S, along flying direction. Signs 0,, 0, denote 
thetiltangles of. P,, P,. Signs f5, f, , f, and f, denote the 
= 
principal-distances of P, , P, , P, and the equivalent 
> 
image P, respectively. The captured images are in the position 
of P,, B, P, (left-tilt P,, horizontal P, and right-tilt. P, ). 
  
  
  
  
Fig.4 Illustration of images Fig.5: projecting center 
conversation displacement 
Assume that the flying direction is X coordinate axis. AS, is 
the projecting center displacement between two adjacent 
camera , ie. $5, and S,,Sjand S, Then, according to the 
principle of collinear equation, the transforming expression 
from À to Pis 
x, = EE 2- 
| A 2 
|». = ft 
f, 
The transforming expression from P, to P,is: 
| f % +AS 
xou TAS. 
J : ? y, sing, + £, cosd, *. (Q2) 
. y,co88, — £ sind, 
yg m fy ————————- 
* ys sin, * f, cos d, 
The transforming expression from P, to À is: 
X: 
Xo = fy mere = AS, 
¥; sind, + f; cosd, (2-3) 
f y, cos), — f, sin, 
Mfg 7 ; 
y, sin6, + f, cos0, 
Because practically, we are unable to position 3 cameras’ 
projecting centers at exactly the same point in space, the 
projecting center displacement (See Fig.5) from second and 
third camera to middle camera AS, needs to be added to 
formula (2-2) and subtracted from (2-3). 
In 3-camera combination scheme, the field of view (FOV) of 
whole photography system is enlarged 3 times of a single 
camera in the direction vertical to flight. But the FOV along 
flying direction remains no change (Actually it shrinks.). So 
the longitudinal overlap should be increased in the course of 
aerial photography. In general, it is easier to control 
longitudinal overlap than lateral overlap. Hence, this method 
is practicable. 
2.2 4-camera combination scheme 
1).Structure 
Other than the structure of 3-camera combination, in the 
4-camera combination scheme, each camera ought to tilt 
outwards a certain angle so that the overall FOV is expanded 
in both X and Y directions. That is, each camera has to rotate 
angles 0, ,Oy round X, Y coordinate axis respectively, as 
shown in Fig. 6,,6,. In such a structure, the 4 cameras’ 
projecting centers form a square, with their principal optical 
a? 
axes tilting fixed angle along designed directions. 
| ! 
f. Le fa ET 
R 4 P B M % P. 
| 
GRUT pepe UAE x UN Dn Ea y 
+ ST Fry Trey 4 ; ri 
= MC rY et Oo. o r^ TTT d 
Ja Vp 
Fig. 6: Camera tilt in 4-camera combination scheme 
The geometry shape of the 4 original images from 4-camera 
system is like the solid lines in Fig. 7. And after the 
rectification of them and mosaic them, the equivalent image is 
like the dash lines in Fig. 7 It shows that the virtual principal 
optical axis of the equivalent image F,is perpendicular to 
horizontal plane, while the four actual principal optical axes 
corresponding to the four cameras are biased +0,,+0,, from 
the virtual Pre axis. Fig. 8 shows the analytical 
0, in vector form. 
expression of y 
Ww x 
0. 0, 
Fig. 7: Original and equivalent images — Fig. 8: Bias of actual 
principal optical axes 
2). Image conversion in 4-camera system 
The image conversation from P, , P5, P, and P, into 
  
    
  
  
   
  
  
   
      
    
   
   
  
  
  
  
   
    
    
   
    
  
   
   
   
     
  
    
    
    
   
       
   
  
   
  
   
    
  
    
   
    
    
  
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