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Mapping without the sun
Zhang, Jixian

but this model needs high-precision attitudes parameters of plat;
the equivalent collinearity equation considered the
characteristics of range projection and influence factors of
image deformations which is equivalent to express by attitude
angles, but this model is not considered the SAR imaging
principles and the parameters needed to solute are much more;
the parallax and elevation relation model is often seen in
documents, but this method has few expressions.
This paper described the method which solutes the three-
dimensional coordinates may be one of them. In this model,
firstly, image distortion caused by factors other than elevation is
corrected by range formulation. Secondly, polynomial
parameters could be calculated by control points. Finally, the
model formulations could be established by correspondence
points on stereo image pairs, and the three-dimensional
coordinates can be got by iterative computation.
Researcher G.M Huang of CASM(Chinese Academy of
Surveying and mapping) has used the correction of projection
difference of photogrammetry to the fields of SAR image
correction and DEM generation txl[10] .This method can be called
polynomial orthorectification model. The study method and
improvement of calculation flow are given based on this theory.
Displacement of radar image caused by terrain can be displayed
in Fig.l. The altitude of ground point P is h , and P' is a
plotted point of P on the reference surface. So, displacement of
images Ax caused by topographic relief can be approximately
described as following equation 1101 :
Ax*-h(H-h)/R/s (1)
Where h — altitude of ground point
H = height of SAR platform
R = distance between radar and ground point
5 = slant range resolution
SAR adopts side-looking imaging mode. In this paper, x axis is
arranged to point to the side-looking direction, so height
displacement influence only x, and there is no difference from
the normal polynomial function in direction y. So, when we use
stereo image pairs to generate DEM, there are two polynomial
orthorectification models for each group of correspondence
points, and the functions can be expressed as follows:
x, =a l0 + a n X+a l2 Y+a n X 2 + a l4 XY+a, 5 Y 2 +(H, -h-h 2 )/R, /s,
y, =b l0 +b n X+b n Y+b n X 2 +b l4 XY+b, 5 Y 2
x r =a r0 +a rl X + a r2 Y+a ri X 2 +a r4 XY+a r5 Y 2 +(H r • h-h 2 )/R r /s r
y r ~b r o +b rl X+b r2 Y+b ri X 2 +b r4 XY+b r5 Y 2
An calculation flow of (2) had been designed in the literature 181 ,
and an experiment of this model had been done by Radarsat
images. However, that calculation flow is much more complex,
and residual error was considered in projection difference due
to doing iterative calculation of two images separately. So,
when it is used in airborne SAR images, the result is not
convergent. Thus, an improvement of the calculation flow has
been done in this paper, and the ground point coordinates (X,
Y , h ) of correspondence points can be got by unite
adjustment method. The details of process steps can be
described as follows:
(D Confirm the initial values ( X° , Y° , h° ) of three
unknowns (X, Y, h). The barycentric coordinates of all control
points are regarded as the initial values in this paper.
® According to principle of indirect adjustment method,
error equations can be established by image coordinates of
correspondence points and approximate coordinates of ground
(D The correction values (dX , dY ,dh) of unknowns can
be calculated according to least square method, and then adding
the iterative correction values of this time to iterative
approximate values of last time to get new values of unknowns.
(D Comparing correction values of unknowns with tolerance,
if they are smaller than tolerance, iterate calculation should be
finished; or new values of unknowns should be regarded as
approximate values, and repeat the process steps (2)—(3) until
meeting tolerance. The tolerance can be 0.1 time of SAR image
Image data used for the study are offered by the No. 704th
Research Institute of China Aeprospace Times Electronics
Corporation. The experimental area is located in ShanXi
province, where the relief is loessial plateau and the height
difference is about 450 m.
According to experimental necessary, there are totally 7 flight
lines. The images obtained by flight lines 5, 9, 14 are adopted in
this paper, whose initial slants are 10500 m, 10000 m, and
10750 m. The height of platform is about 4000 m and the
resolution of images is 1 m. Flight lines 5 and 9 are planed from
west to east and side-looking direction is north; Flight line 14 is
planed from east to west and side-looking direction is south. In
this experiment, same side stereo pairs are composed by images
obtained by flight lines 5 and 9; opposite side stereo pairs are
composed by images obtained by flight lines 9 and 14.
The hue and distortion between the same side stereo image
pairs are similar, so it is easy to select the correspondence
points. However, the hue and distortion between opposite side
stereo image pairs are different, because the direction of
shadow of the two image pairs is opposite (Figure2).