The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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* 2 Y*ÓÌ 
B 4j{yo) 
(3) 
where (Ax, Ay) is the shift in image space, x 0 , yo are the 
approximate image coordinates. Parameters 5„ which define the 
transformation, are determined using some form of ground 
control. The standard approach is to use conventional GCPs. 
The alternative method proposed in this paper (section 3) is to 
use the SRTM-DEM. 
The equations presented above do the projection from object 
space (in UTM coordinates) to image space. They can be easily 
adapted to do the inverse projection, provided that the terrain 
height is known. When a DEM is available this becomes an 
iterative process (Spotimage, 2004) 
2.2 Registration of Forwards and Backwards images 
Forwards (F) and Backwards (B) images suffer much larger 
relief effects. The approach followed in the approximate sensor 
model consists in register these two images to the Nadir image 
and determine y coordinate displacements, and relate them to 
heights. 
The registration is done by means of the affine formulas that 
convert from image to UTM coordinates (also provided for 
images F and B). There is essentially the displacement in y 
direction, according to terrain elevation. A set of tie points were 
identified manually in order to assess those differences. Table 1 
contains the statistics of the differences in x and y image 
coordinates, in pixel units. 
F-N 
B-N 
Ax 
Ay 
Ax 
Ay 
Minimum 
-4.9 
51.2 
-1.9 
-215.5 
Maximum 
-2.8 
271.5 
0.7 
56.6 
Mean 
-3.8 
134.9 
0.3 
-77.7 
Std. Dev. 
0.48 
57.0 
0.56 
56.6 
Table 1. Statistics of differences between image coordinates of 
tie-points between images F and N and B and N. 
In the case of the x coordinate there was a systematic shift of a 
few pixels between Forward and Nadir images. This 
corresponds to a need of a relative orientation, which in 
approximate terms can be seen as the shift in x coordinate. 
With the images in this form it is now simple to determine 
conjugate points by stereo-matching, with a search space in y 
direction. 
described in section 3. Planimetric coordinates of GCPs were 
measured on orthophotos of 0.5 m resolution. Elevations were 
obtained from a 10 m grid DEM, derived photogrametrically for 
1:10,000 scale mapping, with an expected accuracy better than 
2 meters. 
A total of 56 GCPs were projected onto image space with 
correction of relief displacement. Then the correction in image 
space (affine transformation, equation 3) was determined by 
least squares adjustment. A mean displacement of 80 meters 
was needed). Table 2 contains the statistics of the residuals 
obtained in the planimetric adjustment (image residuals, R x R y , 
expressed in meters). 
Image coordinates were also measured on images F and B, for a 
total of 45 GCPs (common to the 3 images) and displacements 
in y direction were calculated. They were plotted against 
heights and a first degree polynomial was determined by least 
squares. Table 2 also contains the statistics of the residuals in 
the linear regression (heights in metes). 
Rx (m) 
Ry(m) 
Rh(m) 
Std. Dev. 
1.6 
1.3 
2.6 
Minimum 
-4.6 
-3.6 
-6.3 
Maximum 
3.3 
2.3 
7.9 
Table 2. Statistics of the residuals obtained in the horizontal 
coordinate adjustment and on the calibration of the 
linear relation between parallax and height. 
Figure 3 contains that plot of the y displacements (between F 
and B images) and heights. The linear relation determined is 
also in Figure 3. 
1200 
• 
** 
•* 
400 
1' :5060-/' 4 1 
0 
0 50 100 150 200 260 300 350 400 450 500 
ParaRax (pixels) 
Figure 3. Graphical representation of heights against 
y-parallaxes, for a total of 45 GCPs 
In order to determine heights a calibration of the relation 
between terrain elevation and y displacement is needed. 
According to the particular situation of very narrow field of 
view of the push-broom scanners, the small terrain height 
relative to the satellite altitude and the small variations in sensor 
attitude during the acquisition of an image, it can be expected 
that this relation is approximately linear. Using a set of GCPs it 
is possible to calibrate this relation. 
2.3 Assessment of the sensor model using GCPs 
A set of control points were used in order to assess the sensor 
model and to be used as check points in the methodology 
3. ALTERNATIVE ORIENTATION USING SRTM-DEM 
3.1 Description of the method 
The alternative method proposed makes use of The SRTM- 
DEM, instead of standard GCPs, in order to correct image 
orientation. From the image header it is possible to extract 
information for the correction of relief displacement in the nadir 
image. It is expected that the adjustment required after that is 
smaller than 100 m. The steps of the method are described 
below: