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3 ADVANTAGES OF 2D AFFINE PROJECTION MODEL
2D affine projection model has superior characteristics due to the simple forms. Firstly, the model is quite
robust and stable for image orientation and triangulation even without prior orbit information because of the
linearity. Secondly, the higher spatial resolution of satellite imagery become, the more efficient this model will
be in point of precision. Okamoto et al (1999) showed with orientation results of SPOT imagery and MOMS-2p
one that the precision of this model corresponds well to that of central projection-based method. A further
important point is that 2D affine projection model is very suitable for mapping. Image coordinates can be
rapidly calculated from giving ground coordinates and orientation parameters.
3.1 Real-time Positioning
Stereo-plotter usually accepts ground coordinates X,Y,Z as input and the corresponding image coordinates
are calculated for image positioning controls. In conventional aerial photograph, the image coordinates can be
‘directly calculated by the collinearity equations. On the contrary, as the exterior orientation parameters of
satellite imagery are described as a function of the image line number i, which is initially unknown, an initial
approximation of image coordinate must be gradually refined by iterations. Whereas the collinearity equations
for a pair of aerial photographs require 24 computer multiplications to transform ground coordinates to image
coordinates, rigorous 1D central perspective approaches for a pair of satellite images require between 300 and
500 computer multiplications (Gugan, 1987). For the real-time image positioning on digital stereo-plotter, the
number of computer multiplications must be reduced.
Fitting to a polynomial equation with small number of terms is an efficient approach (Kratky, 1989). But,
2D affine projection model is faster than Kratky's fitting model. The same process requires only 20 multipli
cations. If the translations from original imagery to affine imagery are carried out in advance, the number of
multiplications is reduced to only 12.
3.2 Generation of Ortho-Image with Existing DTMs
With existing D'TMs, ortho-image can be generated from single satellite image. The ground coordinates of object
field are given by DTMs and the corresponding image coordinates are computed by collinearity equations. In
1D central perspective model, however, image coordinates are acquired by iterative calculation as discussed in
the previous sections. 2D affine projection model has an advantage here again, which the image coordinates
can be directly calculated by the collinearity equations. Figure 1 indicates the essential features of the process.
Ground Truth/GPS Surveying Satellite Image Acquisition/Transfer
Satellite Images
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Figure 1: Scheme for ortho-image production from satellite imagery
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3.3 Generation of Ortho-Image without DTMs
In case of ortho-image generation without existing DTMs, the necessary DTMs must be acquired via stereo
matching methods. The sequence of the operations is followed: epipolar resampling, stereo matching and,
674 International Archives of Photogrammetry and Remote Sensing. Vol.. XXXIII, Part B3. Amsterdam 2000.
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