The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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the actual centre as far as possible; (3) the points detected are to calculate edge intensity and Canny operator to calculate edge 
relative with the actual edge points one by one, it is also to say intensity, which can be described as follows 141 : 
that the width of edge should be a single pixel. 
Canny detector uses the first order gauss differential coefficient 
to seek good balance between noise abatement and the edge 
detection, and its expression is similar to first derivative of 
gauss function. Suppose G(x,y) as the two-dimensional gauss 
function, and f(x,y) as the image, the edge intensity and 
direction of Canny detector can be obtained as follow 
expressions: 
Edge intensity : 
:C(x,y)=\VG*f(x,y)\ 
(1) 
Edge direction 
. n VG*f(x,y) 
(2) 
\VG*f(x,y)\ 
However, there is no CFAR (constant false alarm rate) in SAR 
image for Canny detector, and the CFAR in high-brightness 
area is higher than low-brightness area. Therefore, Canny 
detector can’t be used in SAR image edge detection directly 141 . 
2.2 Ratio Detector 
Touzi and his partners proposed that there is a CFAR 
characteristic for Ratio operator in Gamma distribution coherent 
speckle 51 ,and using this algorithm to generate SAR image edge 
can get a higher precise. The main principle can be described as 
follows: in the glide detection window, getting the central pixel 
point as the detecting object, calculate the sample averages Ui 
and u 2 in non-overlapping region of both sides along a certain 
line direction which passes this point (Note: suppose that the 
image data are 32 - bit intensity values; if the actual data are the 
16 - bit range values, their mean square values should be used). 
Calculate the ratio(R) of two averages, and choose a smaller 
value larger than one from R and R" 1 as r. By the definition, we 
can know that if r tends to one, the average values of two 
regions are closer, and the objects of two areas are more likely 
same; Otherwise, if r tends to zero, the objects of two areas are 
more likely different, and the point to be detected maybe at the 
edge of two regions. 
Given the edge different orientations, along four directions 
shown in Figure 1, each point should be detected, and reserve 
the smallest r value as the result. The neighborhood of Ratio 
operator shouldn’t too big, because the bigger neighborhood 
can only detect the wide edge. As a rule, the neighborhood of 
Ratio operator is 5x5. The edge intensity and direction of Ratio 
detector can be obtained as follow expressions: 
Edge intensity: R[~l /Min(r) (3) 
Edge direction: normal direction of corresponding straight line 
L 
Edge intensity : R L =1 /Min(r) 
(4) 
n .. VG*f(x,y) 
Edge direction : n = 
(5) 
\VG*f(x,y)\ 
(b) Vertical direction; 
(c) Right-leaning 45 degrees; (d) Left-leaning 45 degrees 
Figure 1 Four different detecting directions of Ratio operator 
3. ESTABLISHMENT OF “VIRTUAL EPIPOLAR” 
FUCTION 
In computer vision field, epipolar is called “the polar line”, and 
plays an important part in stereo process of remote sensing. 
However, due to the difference of imaging mechanism between 
SAR and optical image, it is difficult to understand when 
epipolar surface and epipolar line are established in SAR 
images. However, during making geometry rectification or 
generating DEM by SAR images, oblique distance projection 
can be transformed to central projection, and then “equivalent 
collinear equations” of SAR images can be established. In this 
condition, SAR images can build their own “equivalent epipolar 
equations” as the optical images to be used in image match. To 
distinguish the definition of “epipolar” in optical images, 
“virtual epipolar” line is called in this paper. 
Many methods can be used to confirm the “epipolar ”, and they 
are mainly divided into two kinds: one is based on the 
geometric correction of digital image; the other one on coplanar 
conditions 161 . If there are some ground control points, the 
equivalent elements of orientation can be got by collinear 
equation, and then the equivalent “epipolar equations” can be 
established. When it is difficult to get elements of interior 
orientation or only a part of the image should be dealt with, the 
RLT (relative orientation linear transformation) algorithm based 
on coplanar condition can be used to establish corresponding 
epipolar. Its expression can be described as follows 161 : 
2.3 The Integrative Edge Detector q = I% + I^x + I^y + I? 4 x' + I? 5 xx' + I? 6 xy' + I^yx' + I^yy' (6) 
In order to make the edge detector with CFAR and a good 
direction, the edge direction can be calculated separately. 
Whether the edge operator with CFAR or not is determined by 
edge intensity. Therefore, the new detector using Ratio operator