described as
er^ Meo Wi
d X. /
Y E. (13)
— 7
T = cH
ver ee mel | em
Observing the point P(X, Y Z) on the scaled
ground surface with respect to the picture coordinate
system (X, Y, Z) wecan find the corresponding affine
image point Da(Xa, Ya) in the form
Xa > (X - X,j)cos p
via uus (14)
Ya — (X - Yypsin wsin (Y -Yj)cos 0)
Next, we will consider image errors which cannot be
avoided in this image transformation. The image
transformation errors of the first type are caused by the
errors of the given orientation parameters and those of
the second type by height differences in the photo-
graphed terrain. The exterior orientation parameters
(W, §) and the interior ones (XH, ŸH, C) of satellite
photographs are usually given with very accurate
approximations. Thus, the image transformation errors
of the first type are considered to be small. Also, these
errors can be modeled in a linear form, if the deviations
of the orientation parameters are small. This means
that the errors of the first type can be corrected
automatically in the orientation calculation using
Equation 1, because coefficients describing these errors
are absorbed by the orientation parameters Aj (1=1,
---, 8) . On the other hand, the image transformation
errors of the second type increase with the height
difference and distribute almost randomly over the
terrain. Thus, these errors must be removed by
developing an appropriate correction method. As for
the correction technique, an iterative orientation
calculation may be the most pertinent one, where the
image transformation error of each ground point is
corrected by changing the principal distance of the
camera, corresponding to its height difference from the
average height obtained in the previous iteration step.
TESTS WITH A SIMULATED EXAMPLE
The proposed orientation method of satellite CCD
camera imagery was tested with a simulated example.
For the construction of the simulation model 22
satellite CCD camera images are assumed to be taken
consecutively in a convergent manner (See Figure-5.).
The image coordinates of 63 object points were
614
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996
H=850km
Figure-5 : satellite CCD camera images taken con-
secutively in a convergent manner
calculated by means of the collinearity equations under
the following conditions:
flying height of the satellite: H = 700 km
focal length of the used CCD camera : c = 300 mm
picture scale: 1/2,300,000
convergent angles : + 30 degrees
CCD pixel size : 5 um Xx5 jm
number of CCD pixels : 4,000,000
maximum height differences in
the photographed terrains : 100m, 2000m, 4,000m
The perturbed image coordinates were provided in
which the perturbation consisted of random normal
deviates having a standard deviation of 2.0 micrometers.
In the orientation calculation, maximum errors of the
orientation parameters were assumed to be 1 degree for
the rotation parameters, 1000m for the translation
parameters, and Imm for the interior orientation
elements. Also, the arrangement of ground control
points and check points is shown in Figure-6. The
Q : ckeck points © : control point
Figure-6 : configuration of check and control points
obtained results regarding the standard error of unit
weight, the average internal and external errors are given
in Tables-1. From these results we can discuss the
characteristics of the proposed orientation approach of
satellite CCD camera imagery as follows:
1) The field angle of the CCD camera in this case is
about 2 degrees. With such a narrow field angle,
the image transformation errors due to height
differences in the terrain give almost no influences
on the external accuracy, even though the
maximum height difference amounts to 2,000
meters.
2) The external error approaches the theoretical one,
3)
CO
met
affi
Cort
the
orie
exa
con
RE
/17
