The result of a simple approximation is
1 ^ nadir
| = int 3-4
hd E x #tany-(hy=7) S n
and
fh y,/IFOV
F (3-9)
The pixel number in the column i is independent of the
CCD-line (forward, backward, nadir) chosen. Therefore
the geometrical correction creates epipolar-like images.
Figure 3 shows subsamples (400x700 pixels) of the image
in Figure 1. The left image is without correction and the
right image is the result of the geometric correction. The
figure shows that blurring effects in the uncorrected image
can be fully compensated by the pixel ordering procedure
as described previously. The differences in length of the
image strip are caused by the pitch movement.
4. HEIGHT MEASUREMENT IN GEOMETRI-
CALLY CORRECTED IMAGES
The geometric relation after geometric correction is shown
in the following figure.
|
flight direction
terrain
X >
|
Figure 4 Geometric relation for stereo measurement
Figure 4 shows the pixel shift in a corrected image com-
pared to the ideal and real image in the direction of the
flight.
The disturbed ray from a pixel characterized by (Xp: Xd )
intersects the reference plane in X, 2; 7 0.
The row difference between two corrected image strips,
starting at the same point, is proportional to the height of
the object point. The error of this measurement depends
on the chosen reference plane and the attitude distur-
bance.
The corrected point x is shifted accordingly by the differ-
ence between the corrected and ideal image point
ôx = x —xk . The pixel xd sees the terrain point x? on
an undisturbed flight path. This difference can be calcu-
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
lated using the relation between XO and X, and leads to:
0
X X
5x = 20. Ex (4-1)
a z
d
The shift àx is zero if the height of the object point is equal
to the height of the reference plane and/or if the attitude
disturbance is zero.
If the flight path for each corrected image strip is the same,
then the difference between the rows of the two corrected
image strips is proportional to the height of the inspected
image. The true height depends on the reference plane
and the flight disturbance. Different attitude parameters
give therefore different corrected images.
Only a correction on the real DEM gives a corrected image
independent of attitude parameters.
The height in an ideal undisturbed image can be simply
derived from the row difference in a forward and nadir
image, for example (see Figure 5)
h,- 0x, — AX
ze Ang fn
Ax 7 (hi- hi): 9x4 ^ as vue) (4-2)
; wl ui. you
with X4 = Xa 2g Xd 7 tany
results in
AX
fn
hi cu any (4-3)
AX
«1 ———— —— ———— — — »-
AX
óX, i fn ] | OXn
4 4 >
Figure 5 Row difference in an ideal and a corrected image
In the geometrically corrected image an additional part
coming from the correction (4-1) influences the result (4-2)
and gives a column difference (see Figure 5)
AX = AXın + OX; 8X, - (4-4)
This leads to a corrected value for the height
h,: 6X ,—AX
h; = A. (4-5)
28X d ox d
with the correction
x x n
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