ISPRS Commission III, Vol.34, Part 3A „Photogrammetric Computer Vision“, Graz, 2002 
  
R11 
TPO1 
+ 
TP02 TP03 
* + 
TP12 
TPO4 * 
* 
TP08 
TFOS TPos PC 
TP07 
Po 
TRO6 gl 
  
  
  
Figure 10 — Distribution of the SAR-SPOT tie points obtained 
Table 1 contains the estimated coefficient A (in meters of height 
per pixel of parallax), the parallaxes and the corresponding 
heights calculated by equation 10. Heights measured from maps 
and the difference between the two heights (dH) are listed for 
10 of the points. 
Table 1 — Calculation of heights from parallaxes, for the tie- 
points, and comparison with heights measured from topographic 
maps. 
  
  
44 Height determination of the SAR-SPOT tie-points 
If the SPOT orientation parameters used in the image-to-image 
registration were exact the two images would coincide for 
points on the ellipsoid. If the point has a height H above the 
ellipsoid there will be a parallax in x direction, which relates to 
height according to equation 7: 
H= A(x,y)- D. (7) 
where (x,y) are the pixel coordinates on the SPOT image and p, 
is the x-parallax. Coefficient A is not constant along the overlap 
area of the images. If only approximate orientation parameters 
are known for the SPOT image, as is the case when they are 
derived from the header data, there will be a bias coefficient 
(equation 8). 
H = A(x, y)-p, + B(x, y) (8) 
The method proposed here is based on the fact that coefficient 4 
can be estimated with very good accuracy only using the SPOT 
approximate orientation, in the following steps: 
1. A given point on the SPOT image is projected from image 
to ground, with heights 0 and 1000 m. For a height range 
of this order the planimetric displacement has a linear 
variation with height. 
2. The two points obtained in ground coordinates are 
projected onto the SAR image space 
3. From the SAR image space the two points are brought 
back to the SPOT image space (points P, and P5) 
4. The ratio between the height difference (1000 m) and the 
difference between x coordinate of points P, and P», is the 
coefficient A for that point. 
H (9) 
X) 
  
A= 
Coefficient B must be determined from ground control 
information. In a first approximation it will be assumed as 
constant. Knowing the height of one of the tie-points, 
coefficient B can be determined. 
The 12 points extracted corresponded to individual points or 
water surfaces which are represented in the topographic maps of 
the area (1:25,000 scale). The heights of 11 of the points could 
be measured from contours (10 m interval). 
Using the height of point 02, which corresponds to a small 
reservoir, coefficient B was calculated as 362 m. With the 
calibrated relation, heights were calculated for the other points 
and compared with map heights, for the remaining 10 points. 
  
  
  
  
  
  
TP Á Dx H Her dH 
(m/pixel) | (pixels) (m) (m) (m) 
01 8.52 28.2 602 — v 
02 8.70 76.1 1024 1024 — 
03 8.93 3.4 390 405 -15 
04 8.52 35.0 660 650 10 
05 8.49 47.2 763 746 17 
06 8.36 4.5 400 386 14 
07 8.72 67.5 951 965 -14 
08 8.91 53.1 835 855 -20 
09 8.72 17.3 S13 512 ] 
10 8.34 30.9 620 616 4 
11 8.89 18.6 528 531 -3 
12 8.67 63.7 915 916 -1 
  
  
For the 10 check points, the RMS error is 12 meters. The 
coordinates of the tie-points in the registered SAR image were 
converted back to the SAR image space (function R^). The 
SAR image-to-object projection was then applied in order to 
calculate geographic coordinates of the tie-points. These points 
became GCPs, which were used in the SPOT image resection. 
The statistics of the residuals obtained in the least squares 
adjustment, expressed in pixel units, are listed in table 2. 
Table 2 - Statistics of the residuals obtained in the SPOT image 
  
  
orientation 
R, (pixels) | R, (pixels) 
Minimum -0.07 -1.20 
Maximum 0.07 1.32 
RMS 0.04 0.70 
  
  
  
  
  
In order to independently check the accuracy of the image 
orientation obtained, the GPS points were used as check-points. 
The statistics of the residuals obtained after projecting the 
points onto the image are listed in table 3. 
Table 3 - Statistics of the residuals found in the check-points 
  
  
  
  
R, (pixels) | R, (pixels) 
Standard dev. 1.01 1.25 
Mean 0.23 1.06 
RMS 1.00 1.60 
  
  
  
The RMS of the residuals correspond to approximately 12 m in 
longitude and 16 m in latitude. 
These figures would have been better if actual GCPs could have 
been used in the SPOT image resection. When analysing the 
spatial distribution of the errors in the heights determined for 
the tie-points (table 1), although they are probably close to the 
best that can be achieved from a SAR-SPOT intersection, it is 
possible to recognise that they are not randomly distributed. 
Figure 11 represents the SPOT image space, with the tie-points 
and arrows in x direction, with sizes proportional to the errors. 
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