Thë International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
The absolute term is l = (/, l 2 / 3 / 4 ) r ; 
The weight matrix is 
P = 
P X ' 0 0 0 
0 Py t o 0 
0 0 p x 0 
o » : 
After the manipulations, (5) can be written as 
A = (D T PD) 1 D T PL 
(6) 
X,Y,Z can be achieved by this equation. 
D and L in (5) and (6) are different with different 
stereoscopic pair. For example with SPOT and Radarsat-1 slant 
range images, the parameters of D and L are 
¿11 = ^14 = ~^( a 3 X l + f a I ) 
¿12 = ^i5 = (Mi + yfej ) 
¿13 = ^16 = ~^( C 3 X 1 + f C l) 
¿2, =C 24 =^ 
d -c -A 
M 22 ^25 ÿ 
d = c =A 
U 23 ^ 26 ^ 
¿3. = ¿ 10 = -2(A r - X s ) 
d n = =-2(P-r s ) 
¿33 = ><„ =-2(Z-Z,) 
/ = x + f a>(X - XJ + b^Y-Y si ) + c t (Z - Z sl ) 
' ' 7 a 3 (X-X„) + b 3 (Y-Y xl ) + c 3 (Z-Z sl ) 
l =0+ . a 2 (* - *„) + (r-y,.) + c,(Z-Z„) 
2 7 a 3 (X - X xl ) + b 3 (Y -Y sl )+c 3 (Z -Z xl ) 
l 3 = (X - Xs Ÿ -{Y - ft) 2 - (Z - Zs) 2 
~(y 2 M y + Ds 0 ) 2 
/ 4 = (a 0 + 0,^2 + a 2 / 2 + a 3 y\ + a t y 2 ) 
- Xv(X - Xs)+Yv(Y -Ys)+ Zv(Z - Zs) 
4. EXPERIMENTS 
4.1 Test Data 
Four space-borne images covering an area in Beijing, China are 
chosen. The statistics of their attributes are shown in table 1. 
The overlap of four images is shown in Figure 2. The overlap of 
these images is up to 50%-100%. 30 gcps and 34 check points 
are manually collected in 1:25000 raster graphic and marked 
with blue triangles and green circles in Figure 2 respectively. 
The center of Beijing city, the Imperial Palace, is marked with a 
red pentacle in Figure 2. Especially, there are 6 gcps and 9 
check points beyond the SPOT4 image, which are not used in 
any computation about the SPOT4 image for ensuring the 
reliability and accuracy of results. 
4.2 Test Results 
In this experiment, six composite stereoscopic pairs have been 
constructed, which are Radarsatl-ERS2, Radarsatl-SPOT4, 
SPOT4-ERS2, SPOT5-ERS2, SPOT5-Radarsatl and 
SPOT5-SPOT4. Gcps are used to finish the orientation of the 
images and check points are used to check the stereo position 
accuracy of six composite stereoscopic pairs. 
The statistics of RMS values of six pairs are shown in table 2. 
The absolute values of maximum and minimum residual error 
are also listed. In table 2, planimetric RMS error values are 
10-26m and altimetric RMS error values are 15-28m. It means 
that the stereo position with composite stereoscopic pairs is 
successful, and its accuracy is equivalent to the stereoscopic 
pair with optical/optical or SAR/SAR images. 
Figure 2. Overlap of four space-borne images and distribution 
of ground control points 
The statistics of some attributes including overlap, intersection 
angle, length of baseline, flying height and base-height ratio are 
listed in table 3 for analyzing the relation between structure of 
the stereoscopic pair and the space intersection accuracy. 
Experiment results in table 2 show that planimetric error of the 
composite stereo position is mainly determined by geometry 
condition of optical image. The planimetric error values of the 
stereoscopic pairs without optical images, such as 
Radarsatl-ERS2, are lower, but those of the stereoscopic pairs 
with optical images are better. And the spatial resolution of the 
optical image is higher, the composite stereo position accuracy 
is better. Obviously planimetric error values of the stereoscopic 
pairs with the SPOT-5 image are lower than other stereoscopic 
pairs with the SPOT-4 image. 
Experiment results in table 2 also show that altimetric error of 
the composite stereo position is mainly determined by geometry 
condition of SAR image. In 6 stereoscopic pairs, the altimetric 
error value of Radarsatl-ERS2 is lowest, and that of 
SPOT5-SPOT4 is highest. And we find the intersection angle 
and base-height ratio of SPOT4-ERS2 are lowest in table 3, but 
its altimetric error value is not highest. 
And altimetric error of the composite stereo position is 
secondarily determined by intersection geometry condition of 
the stereoscopic pair. In the stereoscopic pairs except 
Radarsatl-ERS2 and SPOT5-SPOT4, altimetric error of 
Radarsatl-SPOT4 is lowest and SPOT4-ERS2 is highest. In 
table 3, the intersection angle and base-height ratio of 
Radarsatl-SPOT4 are highest, but those of SPOT4-ERS2 are 
lowest. 
5. CONCLUSIONS 
The geometric aspects and the mathematical treatment for the 
stereoscopic image pair composed of linear array push-broom 
and SAR space-borne images have been introduced in this 
paper. And the geometric equations of the composite 
stereoscopic image pair are deduced in details. Experiment 
results demonstrate that it is feasible to construct stereoscopic 
pair with optical/S AR images, of which the mean RMS value is 
close to stereoscopic pair with optical/optical or SAR/SAR 
images. 
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