In: Wagner W., Szekely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
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Unfortunately, in this way we usually cannot obtain stable re 
sults. To deal with this problem, the ridge estimate is used 
X(k) = (A T PA + kEy'A T PL (10) , 
where P is the weight matrix and k is the regularization parame 
ter. In order to determine for which k the Y-value can get the 
best result, the L-curve method selects different ^-values and 
calculates the corresponding X. So a group of points are ob 
tained: 
(^),^)) = (lg||^r-4,lg||X|| t ) (11) . 
This curve normally is shaped like the letter ‘L’. The optimal 
value of the regularization parameter k is considered to be the 
one corresponding to the comer of the ‘L’, i.e. the point with 
maximum curvature. 
The principle of IMCCV method is different from that of the L- 
curve method. It replaces the ordinary least-square solution with 
(A T PA + E)X = A T PL + E (i2). 
Since both sides of the equation have unknowns, we can only 
solve by using iterative methods. 
A® = (B T PB+E)~\B T PL+X (k -' } ) (13) 
In our test we use the result of L-curve as the initial value of 
IMCCV method. The result will be calculated by solving Eq. 13 
iteratively until the termination condition is satisfied. 
Once the RPC parameters are obtained, we can use them to geo 
code our data. The forward form of the RPC model is adopted. 
For each object points with known latitude and longitude and 
height fetched from our DEM, the corresponding row and col 
umn indices can be calculated. After resampling, the height of 
each point can be acquired. 
4. EXPERIMENTAL RESULTS 
Our test area is around Kuala Kangsar, Malaysia (N4°29'8"- 
N5°04'38", E100°39'33"-E101 °3'25"). The area is rather flat 
along the river, but is flanked by high mountains on both sides. 
The area is strongly vegetated and the elevation ranges from 40 
m up to 1500 m. A TerraSAR-X stripmap image pair acquired 
on September 13 and September 18, 2008, with incidence an 
gles of 21.4° and 42.7° at the scene centers, is used in our expe 
riments. The amplitude images of the scenes are depicted in 
Figure 2. 
The test data was processed using our own radargrammetric 
processor. The results are compared to a DSM created by Info- 
terra’s Pixel Factory™ (Infoterra 2009), to a publically availa 
ble DEM generated by Infoterra (2010), to GPS ground control 
points provided by Infoterra, as well as to the SRTM DEM. 
Table 1 shows the parameters we used for our experiments. The 
search for homologous points starts at the pyramid level 5 with 
40 meters pixel size, subsequently refining the search using 
lower pyramid levels until pyramid level 2 with 5 meters pixel 
size. In higher pyramid levels a smaller correlation window is 
chosen, but in lower pyramid levels the correlation window gets 
bigger. 
Reference image Match image 
Sep. 18, 2009 Sep. 13, 2009 
© DLR/Infoterra © DLR/Infoterra 
Figure 2. TerraS AR-X stereo pair of Kuala Kangsar, Malaysia 
The search size in Y direction is set to be 3 because we found 
that the azimuth parallaxes are very small. As we can see in Ta 
ble 1, the mean correlation value is smaller in lower pyramid le 
vels. This is due to the increasing level of noise in the lower py 
ramid level images. With a mean correlation of only 0.3 in the 
2 nd pyramid level, we can assume the results to be noisy and 
less reliable. 
Table 1. Correlation Parameters 
Level 
Pixel 
size 
Corr. Win 
dow Size 
Search Size 
in Range 
Search Size 
in Azimuth 
Mean Cor 
relation 
5 
40m 
5x5 
11 
3 
0.68 
4 
20m 
7x7 
11 
3 
0.54 
3 
10m 
9x9 
17 
3 
0.41 
2 
5m 
11x11 
17 
3 
0.30 
Figure 3 shows the DSM calculated by Infoterra’s Pixel Facto 
ry™ and by our radargrammetric processor respectively. As we 
can see, some pixels with no height information are masked out, 
appearing white in the Infoterra’s DSM. In our DSM, all pixels 
are reconstructed except a part in the lower left comer, where no 
height information can be obtained. 
The DSM created using Infoterra’s Pixel Factory™ has a mean 
absolute height error of about -1.7 m with a standard deviation 
of 8.4 compared to 26 GPS ground control points. Our DSM 
was generated fully automatically without using any ground 
control points. In this way we got a mean error of -44.2 m and 
standard deviation of 22.88 m. After using one control point, lo 
cated in the middle of the reference image (100.947 E / 4.79557 
N), to correct our results in elevation direction, we got a mean 
error of 2.79 m. Comparing our DSM with Infoterra’s DSM, the 
mean error for the full image is 7.07 m and standard deviation is 
19.97 m. Compared with the newest DEM available from Info 
terra (2010) we have a mean error of -12.64 with a standard 
deviation of 18.84. We also compared our DSM with the SRTM 
DSM and got a mean error of 2.8 m with a standard deviation 
13.6 m.