International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004
polynomial parameters. Secondly, we add height displacement
and finally get true image coordinates.
2. METHODS
It is usual to adopt following expressions for quadratic
polynomial rectification.
x-agtaj Xa; Yay X ^ ta4X Ya, Y?
y=botb; X+b,Y+b1X"+b4XY+b;Y" ( 1 )
Where x,y lis image point coordinates, and correspondingly
X,Y | is its ground point coordinates. a; and b; are unknowns.
In this paper, we introduce height displacement caused by
elevation which is corrected in advance and make use of (2) for
polynomial orthorectification.
x+dx=a,+a; X+a, Y+a;X"+a,XY+asY"
y=bytb,X+b,Y+b,X"+b4XY+b;Y” (2)
Where dx is height displacement caused by elevation.
Displacement of radar image caused by terrain can be displayed
in Fig 1.
> ™ ; : X
!
e R i 1
^
= i 1
^
~ I 1
~
- 1 !
^ J 4
x
x 1
^ /
> /
x
^ /
x
x /
x /
> / z
S 7
A
/ SN
Z SN
Figure 1. Terrain influence to radar image
c
We presume that h is elevation of ground point P', and its image
coordinate is X’= A R', where 4 is imaging scale and P is
projective point in ground datum plane. The slant range of P can
be approximately describes as following equation:
R^ R-hcos Q
Where 9 is the imaging angle of P'. Accordingly, displacement
caused by elevation can be showed as:
dx-X'-X* — Ahcos
Suppose s is ground resolution, and we can realize following
transform:
dx * —hicosO is
where
COS Ü | (H-h)R
SO
dx = -h(H-h)/R/s (3)
Equation 3 is approximate expression of height displacement,
If it needs strict computation, the equation as follows can be
used:
dy z J(U - (0H -hy)e H^ -R
JE TH Men (4)
When there is a biggish Gand ground point is far away from
ground nadir point(for ERS-2 image, when 0is 25 degree, the
distance from ground point to ground nadir point is 323
kilometers), height displacement may be affected by ellipticity
of the earth. We can reduce such affection by correcting datum
plane which includes the correction of slant angle 0 and flight
height. In this way, according to normal of central tangential
plane in cach frame, We can calculate slant angle 0, and change
flight height into distance from imaging center to tangential
plane.
Figure 2. slope correction
Showing as Fig 2: where the earth level surface is regarded as a
sphere O with a semi diameter Re |A is projection of ground
point toward image point in the level surface, and N is ground
nadir point.
We regard 3 as [1AOS. Then, in the surface of AOS, AN' is
tangent of the sphere O across point A, and SN' pass through
point S which is vertical line according to AN'. So N' and. 0'
respectively express the new ground nadir point and slant angle.
Where OB SALB is. intersection of OB and SA . because of
SN'/AOUthen:
EUN
BAO=0'
0'=arcsin[(Re+H)sin0/Re]
H'=ResinBcos(0 B)/sin0
Corrected H' replaces H in formula(3)or (4). It is modified
height displacement corrective formula and expresses as (3) or
(4) in order to convenient for description.
If flight height is unknown, then dx is also unknown, and
expression (2) must be modified.
Thinking of expression (3), the new expression (2)is the follow:
x+h"/R=agt a X+taY+ta; X +a4XY+ a; Y^-H-h/R
y=bg +b; X+b,Y +b; X +b, XY +b Y? (
wh
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