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Mapping without the sun
Zhang, Jixian

/ = det(M) -k* tr 2 (M)
Figure 2. Real SAR image
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)
H(A) = Y,P(A)\og(P(A))
H(A,B) = Y P ( A > B) log (P(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
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
Figure 3. Map
The real SAR i
relationship bet\
SAR image is
Therefore a pi
corresponding si
realization meth