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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
2.3.1 Orbital Parameter Modeling of Ikonos Geo Image
The Keplerian elements ara ea, ) in-flight position
(021575) and viewing angle of the imaging sensor were
approximated from meta data, image file, image acquisition
geometry and celestial mechanics (Sadeghian, 2002).
A simpler and more pragmatic approach was implemented by the
authors to convert Geo image to the corresponding raw image
form. A comparison of the raw and Geo image shows one major
difference in terms of geometry. As noted previously, the number
of pixels per line in the raw image is 13500, while in this Geo
image it is more than 13500. It is because off-nadir view angle of
the image and the image has been rectified and resampled in such
a way that each pixel has a pixel size of 1 m on the ground. With
due attention to this difference, a procedure was devised and
implemented by authors to carry out the required conversion.
The size of the Geo image (rectangle) is different from that of the
corresponding raw image. Two coefficients are now computed to
enable the final image to have the same size (13500 * 13500
pixels) in two directions as a raw image. These coefficients are
used to produce the pixel and line coordinates of each point
respectively from the following expressions:
Coefficient for the p coordinate = 13500/total number of pixels in
each line
Coefficient for the / coordinate = 13500/total line of pixels in
each scene
It will be seen that this procedure is somewhat akin to that of an
affine transformation. However, additional displacements were
introduced into the Geo imagery by the original corrections for
each curvature/panoramic distortion. These displacements occur
predominantly in the cross-track (y) direction and, since they are
approximately symmetrical about the image center line,
parameters adjusting the attitude as a function of the cross-track
image coordinates should give a good correction for these
displacements by replacing the terms in equation (3) by a term for
this purpose, which leads to the following equations:
;
® =O, +X +0,"
2
P= tOX+ PY
K=K,+KX+K,Y" (16)
Where x and y are the image coordinate. These equations have
been incorporated in the procedure to transform the Geo image
coordinates to their raw image form.
3. THE HAMEDAN IKONOS TESTFIELD AND IMAGE
MENSURATION
The Ikonos Geo panchromatic image employed covered an 11 x
15 km area of central Hamedan city in the west of Iran. It was
acquired on 7 October 2000 with a 20.4? off-nadir angle and 47.4?
sun elevations. Carterra Geo products are georectified, which
means that they are rectified to an inflated ellipsoid and selected
projection, in this case UTM on the WGS84 datum. No terrain-
correction model is applied so these images are only rectified, as
opposed to orthorectified. The stated accuracy of the Carterra Geo
products is specified as 50 m CE90 exclusive of terrain
displacement (Grodecki and Dail, 2001 ). In this investigation, the
elevation within the Ikonos test area ranged from 1700 m to 1900
m. The GCPs/ICPs (Independent Check Points) for the tests were
extracted from NCC-product digital maps, which employed a
UTM projection on the WGS84 datum. In this instance the
mapping scale was 1:1000, with the compilation have been carried
out using 1:4000 scale aerial photographs. The selected
GCPs/ICPs in the imagery were distinct features such as building
and pools corners, and wall and roads crossings, etc. The image
coordinates of the GCPs/ICPs were monoscopically measured
using the PCI EASI/PACE software system. These image
measurements were then input into the least-squares adjustment
computations, for the parameters of the DLT, SDLT and 3D affine
as well as into the calculations for the orbital parameter model.
4. PRACTICAL EVALUATION
Non-rigorous transformation computations were carried out with
software written by the first author. Least squares determinations
of the parameters of each orientation model were carried out using
all available GCPs, namely 34 also 20 and 7 for the Ikonos image.
The ground coordinates of ICPs were then determined utilizing the
derived parameters and the differences between the
photogrammetrically determined and map-recorded ground
positions then formed the basis of the accuracy assessment phase.
Tables 1,2,3 and 4 show summaries of the root mean square error
(RMSE) obtained for the series of object point determinations, for
the Ikonos image using polynomials (4. 5 and 6 terms), 2D
projective, 3D affine, DLT, SDLT, rational (14, 17 and 20 terms).
multiquadric (3,6 and 10 terms) and TPS. Where API is
represented as the square root of sum of AE and AN squares.
Table 1. API, RMSE values achieved in UTM coordinates of the
Ikonos data, using polynomial equations
Method GCPs ICPs Control Check
Number | Number Points Points
APl(m) API(m)
34 20 4.24 3.30
4 Term 20 34 4.52 4.02
7 47 1.39 6.61
34 20 3.95 322
5 Term 20 34 4.16 3.73
7 47 1.37 6.46
34 20 1.31 1.56
6 Term 20 34 1:35 1.62
7 47 1.30 9.90
Table 2. API, RMSE values achieved in UTM coordinates of the
Ikonos data over the Hamedan project area
Method GCPs ICPs Control Check
Number | Number Points Points
APl(m) APl(m)
2D 34 20 4.17 2.95
Projective 20 34 4.45 3.20
7 47 1.74 4.4]
3D Affine 34 20 1.02 0.97
20 34 0.96 1.04
7 47 0.91 1.10
34 20 0.95 0.95
DIT 20 34 0.90 0.97
7 47 0.59 1.90
34 20 0.85 0.98
SDLT 20 34 0.82 0.96
7 47 :32 2.69
