International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B1. Istanbul 2004 
  
Fig.. . e-Niteroi bridge band3 (channel 1) image 
e 
original and processed image. 
3.3 Bridge model 
3.°.!  Rio-Niteroi bridge model 
fal 2 the set of integer numbers. Let F be a finite interval 
with an odd number of elements representing a vertical 
iue of the dig ‘4 in which the distance between 
tw- consecutive .> meter for convenience. 
ee abe the of F,. Based on radiometric and 
+ etre te .dge over the Guanabara bay, the 
*»idge mode. a f, on F given by 
ft ixelu- 15m +13] 
AQ) 
Es 
otherwise xeF, 
where s, / are, respectively, the background (water body) 
and the deck radiometry. 
3.3.2 Causeway bridge model 
Let F be a finite interval of Z with an even number of elements 
representing an horizontal line of the digital scene domain in 
which the distance between two consecutive elements is one 
meter for convenience. 
Let uw, be the center point of F,. Based on radiometric and 
geometric features of the bridge over the Pontchartrain Lake, 
the bridge is modeled as the function f on F5 given by 
fi ifxe [us —22,u5 - 13] 
h(x)=4h fxe [us +13, uy + 22] xcfF 
Ss otherwise 
where s, /j, 5 are the background, first deck and second deck 
radiometry information, respectively. 
3.4 Bridge axis identification 
According to Figure 5 and Figure 6, the bridge axis is a straight 
line. Consequently, it can be represented by a linear model. 
Let the bridge image g be a mapping from G = m x n, its 
domain, to K, its gray-scale, where m = [1, mjc Zand n = (1, 
i 
2f 
HO 
$ 
Ÿ 
oe 
ge 
  
original and processed image. 
n] c Z, where m and n are the number of rows and columns of 
the image g, respectively. 
3.4.1 Rio-Niteroi bridge axis identification 
Let ¢; be the mapping from n to m such that c,(/) (j € n) is the 
row number in m, for which g(c,(/), j) is maximum in {g(, 
J)}iem 
Let a, b € R, such that 
s. ((a. y b)- c, (j JY is minimum, 
icem 
then a.j +h (jen) is the bridge center estimation along 
column / 
3.4.2 Causeway bridge axis identification 
Let c; be the mapping from m to n such that c) (i e m) is the 
column number in n, for which g(i, c;(i)) is maximum in {g(/, 
A } jen 
Let a, b € R, such that 
X ((a .i + 5 )- e. (i ) is minimum, 
iem 
then a.i - b. (iem) is the bridge center estimation along row i. 
In both cases (Rio-Niteroi and Causeway bridge axis 
identification), there are more measurements available than 
unknown parameters (a and b) Therefore, the QR- 
decomposition was used to generate a least square solution to 
an over-determined system of linear equations (Kreyszig, 
1993). 
3.5 System point spread function 
The overall CBERS-1 CCD on-orbit PSF is a composition of the 
PSF of each sub-system PSF: optics, detector, electronics, etc. In 
this work the system point spread function is modeled as a 2D 
separable Gaussian function 7, ,, ON F; x F> centered at (uy, 42), 
that is, 
    
   
   
   
  
  
  
   
  
  
    
   
  
  
   
     
    
     
   
    
     
  
  
   
    
    
   
   
  
  
  
   
    
   
   
  
   
  
  
  
  
   
    
   
  
   
Internationc 
where 
h 
and 
h 
3.6 Bridge 
3.6.1 Rio 
The target i 
bridge cent 
transformati 
For a given 
Let Gi, be 
elements, de 
Letv= (pt 
Let assume 
Let 7, bea 
Et 
T, (y): 
where 
ky 
In the abov 
represents h 
shows the R 
362 Ca 
In this simu 
was used al 
center and t] 
For a given 
Let G,, be 
elements, de 
Let assume 
where v = (7 
ks 
In the abov 
represents h