International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part Bl. Istanbul 2004 
  
SAR image 
| line and point detection | 
( optical image 
edge detection 
  
rome 
| matching 
| 
| . i 
| selection of matches | MÀ. 
E T d e building map > 
  
e DTM E = 
i dry caca ee selection of matching | 
L X: 
  
Figure 1: Synopsis of the proposed method. Input data are the 
original SAR image and optical image (knowing the sensor pa- 
rameters) and a map of buildings for the DEM reconstruction 
step. 
dral or trihedral configurations and therefore should be visible on 
the optical data as well. 
2.1 Line detector 
The line detector has previously been proposed in (Tupin et al., 
1998). It is based on the fusion of the results from two line detec- 
tors DI and D2, both taking the statistical properties of speckle 
into account. Both detectors have a constant false-alarm rate - 
CFAR detectors- (that is, the rate of false alarms is independent 
of the average radiometry of the considered region, as defined in 
( Touzi et al., 1988)). Line detector D1 is based on the ratio edge 
detector (Touzi et al., 1988), widely used in coherent imagery as 
stated before. Detector D2 uses the normalized centered corre- 
lation between 2 populations of pixels. Both responses from DI 
and D2 are merged in order to obtain a unique response as well as 
an associated direction for each pixel. The detection results are 
post-processed to provide line segment candidates. 
We just recall here the line detector expressions (a detailed study 
can be found in (Tupin et al., 1998)). The response of the ratio 
edge detector between 2 regions à and j of empirical means p; 
and p; is rij: 
Tj 1— min( 5, Bi 
Pj Mi 
and the response to Dl as r — min(ri2, 13), the minimum re- 
sponse of a ratio edge detector on both sides of the linear struc- 
ture. 
The cross-correlation coefficient p;; between 2 regions 7 and j 
can be shown to be: 
1 
2002 2 
niyicij Y njy 
nin;(cij — 1) 
  
2 
Piz = 
1-F (ni 4 nj) 
where n; is the pixel number in region ?, €; = i“ is the empir- 
j 
ical contrast between regions 2 and j, and y; the variation coef- 
ficient (ratio of standard deviation and mean) which adequately 
     
measures homogeneity in radar imagery scenes. This expression 
depends on the contrast between regions ? and 7, but also takes 
into account the homogeneity of each region, thus being more 
coherent than the ratio detector (which may be influenced by iso- 
lated values). In the case of a homogeneous window pi — pj, 
pi; equals 0 as expected. As for D1, the line detector D2 is de- 
fined by the minimum response p of the filter on both sides of the 
structure: p = min(p12, p23). 
Then both responses are merged using an associative symmetrical 
sum c (z, y), as defined in (Bloch, 1996): 
zy 
rrr re with æ 1 
1-z~-y+2zy wih 2,9 SA 
o(z,y) = 
A theoretical and simulation based study could be used to define 
the adapted threshold depending on a false alarm and a detection 
rate. In fact, due to the unknown distribution of the bright pixels 
along the building / ground corner, such a study is quite difficult 
in this case and the detection threshold has been empirically cho- 
sen. 
The set of detected linear features (i.e segments) will be denoted 
S; in the following. 
2.2 Target detection 
Once again a CFAR detector is used. It has first been proposed by 
Lopes (Lopes et al., 1990) and is based on the ratio of the intensity 
means of the target and the surrounding background. Therefore, 
the moving window is subdivided into two areas, a cross shaped 
area centered on the center of the window and the area resulting 
of the suppression of the cross in the window. 
Again, a theoretical and simulation based study could be used 
to define the adapted threshold depending on a false alarm and 
a detection rate. In fact, due to the unknown distribution of the 
bright pixels of the buildings or man-made objects, an empirical 
threshold of 2 has been used. 
The set of detected punctual features will be denoted S, in the 
following. 
3 PROJECTION AND MATCHING 
3.1 Projection equations 
To project points from optical to SAR data and inversely we need 
some transformation functions. They are based on the computa- 
tion of the 3D coordinates of the point and on the knowledge of 
the sensor acquisition system parameters. 
The principle of the SAR system is based on the emission of elec- 
tromagnetic waves which are then backscattered by the elements 
lying on the ground. For a given time t of acquisition, the imaged 
points lie in the intersection of a sphere of range R = ct and a 
cone related to the depointing of the antenna. More precisely, let 
us denote by S the sensor position, by V the speed of the sensor, 
and by 8p the Doppler angle which is related to the Doppler fre- 
quency fp and the speed by cos(0) — AMD the SAR equations 
= av 
are then given by: 
Sys = I 
Rsin(0p)V = SMNV 
Knowing the line and column j of a pixel and making a height 
hypothesis A, the 3D coordinates of the corresponding point M 
    
      
  
  
  
    
   
   
  
     
   
  
  
   
   
  
   
  
   
   
  
   
  
   
   
    
    
  
  
  
   
   
  
   
   
   
  
   
    
   
   
   
   
   
    
  
   
  
   
  
   
  
  
  
  
  
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