The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part Bl. Beijing 2008 
Where M 9 ,M i = rotate matrix which are denoted by the elements 
of exterior orientation from the i row. 
let M e M i = 
a, 
a, 
b\ b 2 b 3 
so 
x . = f «.V ~ *«) + \(Y - Y si ) + c,'(Z -ZJ 
a^X-X sl ) + b 3 \Y-Y si ) + c 3 \z-Z si ) 
y _ Q f a^{X-X si ) + b^{Y-Y si ) + c^{Z-Z si ) 
Fig 2. Epipolar Geometry of projection track method 
This model is an approximate model which assumes the 
elements of exterior orientation are the linear function of time. 
Through this approximate model, the epipolar geometry could 
be used in SAR image. 
Scholars have put forward several epipolarity models in 
photogrammetry. One is based on the polynomial fitting of 
conjugate points. And, another one based on changing the 
height of the corresponding object point along the light ray is 
named as projection track method [4]. This paper based on 
theory of projection track method. Since looking the SAR 
image as the multi-central projection linear array imagery, 
according to the characteristic of central projection imagery, 
changing the height of the corresponding object point along the 
ray connecting the perspective centre and projecting the object 
points onto the other image, the track of a series of pixels 
obtained is the epipolar curve, then corresponding image points 
could be searched in the epipolar curve. 
3. EXPERIMENT METHOD 
After analyzing the epipolar geometry theory in SAR image, 
the detail approach of the research is as follow steps: 
Firstly, we chose a pair of airborne SAR images. In order to 
improve the effective of matching, the pyramid-layered method 
has been adopted in this research. The bottom of the 
pyramid-image is the original airborne SAR image. The top of 
the pyramid-image is formed by putting together 2*2 pixels 
from the bottom of the pyramid-image. After extracting feature 
points in the left image as control points, we extracted the grid 
points of the left image as the feature points, and computed out 
the coordinate of these points. 
Secondly, we built the SAR imaging equation. Based on the 
imaging model of CCD push-broom imagery, the SAR 
row-center projection equation is built to represent the 
relationship between the image coordinate and space coordinate. 
Assuming that point q(xi,0) is the point in the i scan line of left 
image, so we can construct a function to represent the space 
coordinate of point Q(X,Y,Z), which is in the line of Sq by the 
row-center projection equation(S is the projection center of 
them i scan line)[4]. 
r \\ r U r U 
x, 
(X,Y,Z) T =(X si ,Y si ,Z si ) T +Ä 
r 2 1 r 22 r 23 
/31 ^32 >33 _ 
^ ° 
1 
Where /1 = proportional divisor, 
Tjj = coefficient of rotate matrix in left image, 
(X si , Y si , Z si ) = coordinate of left photographic centre 
If point Q is also projected in the j scan line of right image, the 
space coordinate of point Q would be satisfied the projection 
equation of the right image. 
x f„(x- X'„) + rjy_ - y,')+r 3 ,(z - z; f ) 
f-JX -*')+r a (Y - rj)+r 3J (z - z;.) 
0 = r a (X -X' sj ) + r 22 (Y-Y') + r 32 (Z - Z') 
Where Y~ = coefficient of rotate matrix in right image, 
(X' sj ,Y' S j,Z' S j) coordinate of right photographic 
centre. 
Then using the simultaneous equations to obtain the epipolar 
line equation, the correlativity of left and right image would be 
constructed 
h x r + hy r + h x r y r + ^4 “ 0 
h = m \ y l +m 2 
l 2 = (jn 2) x l + m 4 )y, + (m 5 x, + m 6 ) 
h=m 1 y i +m 8 
l 4 =(m 9 x l +m w )y l +(m n x l +m 12 ) 
Where li(i= 1, • • • 12) is the constant, 
(x r ,y r ) and (xi,yi) are the coordinate of the homologous 
image points 
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