If SIFT or SURF feature descriptors are used it can be 
checked if corresponding features match each other better 
than any other feature (as explained in Wohlfeil, 2010). Much 
better performance has been achieved using the above 
mentioned KLT feature tracker and a special matching 
algorithm that is explained in this contribution. 
3.2.1 Redundant Matching with Consistency Check 
First, in all of N possibly overlapping images, features are 
determined according to Shi and Tomasi (1994). A given 
minimum distance between features limits their number and 
ensures a good distribution. For each of the selected features 
an NxN connectivity matrix C is created with one single 
positive entry at C(i, i) denoting that the position of the 
feature is yet only known in image i. All other entries are 
initialized negative. Also a vector of feature positions F is 
created for every feature with F(i) set to the feature's position 
in image i. Next, the following algorithm is performed, 
written in pseudo code: 
FOR every tuple of images i and j with i # j 
FOR all features with a positive entry in C(i,i) 
Try to track the feature from image i to image j 
(using the KLT feature tracker) to the position f. 
IF tracking was successful 
IF C(j,j) is positive 
IF |F(i) — f| ? d, (with d, — 0.5 pixel) 
Feature positions are inconsistent. Discard feature. 
ELSE 
Set C(ij) positive (tracking from i to j is consistent) 
ENDIF 
ELSE 
Set C(j,j) and C(ij) positive (first tracking from i to j) 
Set F(j) to f 
ENDIF 
ENDIF 
ENDFOR 
ENDFOR 
C is made symmetric by setting all elements C(ijj) negative 
for which the corresponding element C(j,i) is negative (Table 
1). The number c of the remaining positive elements of C is 
then used to calculate the rating 7 = c/N° for every feature. 
3.2.2 Multi Resolution Matching Approach 
In mountainous areas the displacement of features can differ 
by many hundreds or thousands of pixels in different images. 
For the KLT feature tracker such large displacements lead to 
many mismatches. With a simple approach this can be 
avoided. The previously explained feature matching 
algorithm is performed at two levels of image resolution. 
All images are scaled down to a manageable size (~10 
Megapixel) and are matched, resulting in a feature list Fotos 
providing information about the rough relative alignment of 
the different image regions. 
With this information, corresponding image tiles with a 
reasonable size and full resolution can be extracted from the 
original images. The algorithm is then repeated with each of 
these tiles. For all of the performed test it was enough to 
process only 30% well distributed tiles of the whole image 
area to retrieve enough homologous points for a reliable and 
accurate bundle adjustment. More points do not improve the 
results significantly, but unnecessarily increase the 
calculation time 
All features whose offset is larger than the maximum possible 
disparity (according to the limited height range), are regarded 
76 
as outliers and removed from the list. Features showing a 
relatively high deviation (726) are removed as well. 
Finally all features are sorted by descending rating and only 
the best are kept. Despite of the consistency check and 
statistical analysis there can still be a relevant amount of 
incorrect matches among the remaining features. But even in 
challenging situations their number is low enough to detect 
and eliminate them during the bundle adjustment. 
3.3 Bundle Adjustment 
As the positions of the center of projection can be determined 
with sufficient precision via GNSS for every captured line, 
only the errors in orientation determination — the rotational 
offsets between the measured and the real camera rotation - 
have to be determined together with the 3D-positions of 
homologous points. Depending on the platform and the 
orientation measurement system these rotational offsets drift 
slowly over time. These drifts are modeled by an orientation 
correction function, consisting of L = 1..N sets of rotational 
offsets, defined for equidistant points in time and interpolated 
over time via quadratic Bezier curves (Wohlfeil, 2010). The 
temporal distance between the correction parameter sets is 
chosen according to the drift characteristics of the orientation 
measurement error. 
Similar to the adjustment of frame images, the appropriate 
parameters of all rotational offsets are determined with the 
help of the selected homologous points. While the correction 
of a frame image’s orientation is typically expressed by a 
single spatial rotation, the orientation correction function of a 
line image has more correction parameters. In both cases 
correction parameters have to be found that meet best the 
collinearity constraints for all homologous points. 
The C implementation of sparse bundle adjustment from 
(Lourakis and Argyros, 2004) is used for performing this 
task. Due to errors in the automatically determined 
homologous points, bundle adjustment must be performed 
repeated in order to detect and eliminate incorrect points. 
They are detected due to their residuals, which are 
significantly larger than the RMS of all residuals. In practice, 
a threshold of three times the RMS worked well in all cases. 
3.4 Preventing loss of the absolute orientation 
After bundle adjustment with homologous points, the relative 
orientation of the involved images is optimal. But if no 
information about the measured absolute orientation of the 
images is given to the bundle adjustment, the accuracy of this 
orientation can get lost. This is especially the case for remote 
sensing satellites with a small field of view, such as most 
high resolution sensors with a narrow swath (i.e. few 
kilometers). Due to the small field of view and the large 
distance of the satellite from the earth, the rays of light 
corresponding to different pixels of the image are almost 
parallel. Due to that, the error function is very flat in terms of 
the absolute orientation. As a result, very small errors in the 
positions of the homologous points cause the absolute 
orientation to drift far away. 
This can be prevented by integrating ground control points 
(with known positions in object space) in the bundle 
adjustment. But the measurement of their positions is very 
laborious and not always possible. 
The problem is solved by using a small subset of homologous 
points remaining after bundle adjustment as pseudo ground 
control points. Their position is determined by spatial 
intersection of corresponding lines of sight, using the directly 
measured orientation. Finally, one additional bundle 
adju 
and 
of a 
geo- 
whi 
coni 
3.5 
Afte 
orie 
dete 
orie 
etc. 
SG 
of € 
ima; 
the | 
mus 
auto 
how 
line 
curv 
ima, 
orie 
capt 
can 
plan 
d (c, 
and 
This 
any 
of a 
poir 
ovel 
The 
to n 
the ‘ 
dow 
GSI 
mea 
hom 
can 
reso 
3.6 
The 
extr. 
wat: 
only 
the 
solu 
num 
Fort 
wat 
elev 
area 
poir 
dila 
sim] 
The 
cont 
disa 
vola 
user