/ = det(M) -k* tr 2 (M) 
Figure 2. Real SAR image 
3. EXTRACTING HOMOLOGOUS FEATURE POINTS 
(2) 
where det is the determinant of the matrix and tr is the trace of 
the matrix, while k is a default constant between 0.4 and 0.6. 
The simple derivative in height and width direction and their 
multiply are calculated pixel by pixel, then the interest value of 
each pixel is calculated. The feature point extracted by Harris 
algorithm is a pixel whose interest value is local maximum in 
its neighbour region. Therefore the points whose interest values 
are local maximum are extracted from the raw image. In 
practice we use a 3x3 window whose centre is current pixel to 
extract local maximum. Harris operator is an effective operator 
to extract feature points, and its advantages are: (1) easy 
calculation. Only simple difference gray level is used and no 
threshold is needed, so it is automatic. (2)The distribution of 
feature points is reasonable because the interest value of each 
pixel is calculated and then optimal point is selected in its 
neighbours. (3) Harris operator is a stable operator because of 
its simple derivative and no threshold. 
3.2 Homologous feature points extracted by matching 
It is necessary to determine the mapping relationship between 
DEM and real SAR image in order to ortho-rectify SAR, but it 
is impossible to build their relationship directly and we can 
only map the real SAR image to DEM indirectly by means of 
simulated SAR image if the real SAR image is registered with 
simulated SAR image accurately, because the mapping 
relationship between simulated image and DEM is founded by 
simulating SAR pixel by pixel. 
Image registration is a research focus in the field of image 
processing and now it is very difficult to register two images 
automatically. We utilize a method to register real SAR image 
with simulated SAR image from coarse registration to fine 
registration. Coarse registration is executed by polynomial 
using 4~6 homologous feature points selected in simulated SAR 
and real SAR images manually in order to unify the scale and 
rotation between them and then lots of homologous feature 
points are extracted automatically in two images in order to 
realize fine registration. The feature point is first extracted in 
simulated SAR image and then homologous feature point is 
searched by matching simulated SAR with the real SAR image. 
3.1 Extracting feature points by Harris detector 
There are some detectors proposed to extract feature points in 
image such as Moravec and Forstner operator. Harris detector is 
proposed by C. Harris (Harris, 1988) and it utilizes the matrix M 
related to self-correlation function because matrix M is the 
simple ratio to self-correlation function. The point should be 
regarded as a feature point if the value of two curve ratio is 
very high. The matrix M is calculated as follows: 
Homologous feature points in real SAR image should be found 
after lots of feature points are extracted in simulated SAR 
image. These homologous points in the real SAR image can be 
searched in a small window because of coarse registration, 
template matching by mutual information is a useful method to 
extract homologous points successfully. 
Mutual information is a basic concept in information theory and 
it is used to describe the statistical mutuality between two 
systems(Chen,2003). Registering medical images by mutual 
information achieves good effects and it has been widely used, 
because mutual information is calculated using the statistical 
information of image and there is no restriction in gray level 
value and no prepare processing. Two dimension histogram of 
image pair, i.e. joint histogram is used in addition to the image 
histogram. We use the normalized mutual information: 
j = H(A) + H(B)-H(A,B) (3) 
H(A) + H(B) 
where 
H(A) = Y,P(A)\og(P(A)) 
A 
B 
H(A,B) = Y P ( A > B) log (P(A, B)) 
A,B 
£fr 2 (r,c) £f r (r,c)-f c (r, c ) 
£f r (r,c)-f c (r,c) £f c 2 (r, c ) 
where f (r, C) is gradient in height direction and 
f (r, C) is gradient in width direction, and the interest value I 
is calculated using following formula : 
and P(A),P(B) are histogram of image A and B respectively 
while P(A,B) is the joint histogram of two images. 
The mutual information will be maximum if the two images are 
registered finely, so the value of mutual information is searched 
step by step until the maximum is found, then two images is 
registered finely. 
In practice of extracting the homologous points, we will 
intercept a window image(such as 64x64) whose center is the 
feature point in the simulated SAR image, and then its 
corresponding lc 
the coefficient ol 
the real SAR im< 
window in the si 
until the maxirr 
corresponding lo 
4. ORTHO-F 
Lots of homolc 
simulated SAR i 
control for fine 
points between t 
be used to build 
ideal solution t< 
these homologoi 
regions one by c 
construct many t 
(TIN). The verti 
can cover the wl 
the vertices of tv 
pixels within the 
Therefore the sii 
image finely. Fij 
one triangle in 
image as well 
simulated SAR i 
Triangle in real SAR 
Creating 
trans 
Figure 3. Map 
The real SAR i 
relationship bet\ 
SAR image is 
Therefore a pi 
corresponding 
corresponding si 
realization meth 
detail.