International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B4. Istanbul 2004
Figure 4: DTM of Valles Marineris derived from MOLA tracks
3 CONCEPT
In this Section the automated measurement of image coordinates
of tie points applying the matching software hwmatch] of the In-
stitute of Photogrammetry and Geolnformation (IPI) of Univer-
sity of Hannover and the bundle adjustment software hwbundle
of LPF will be described.
3.1 Matching
For automatic extraction of image coordinates of tie points soft-
ware hwmatchl is used. Originally, hwmatchl was developed at
the LPF in Munich for frame images, but the implementation of
the extended functional model for three line imagery (Ebner et
al., 1994) enabled its use also for line sensor imagery. The IPI
modified Awmatchl according to the requirements of the Mars
Express Mission (Heipke et al., 2004).
As input data the matching needs images, the observed exterior
orientation, and the calibrated interior orientation parameters. As
an optional input it is possible to use a MOLA DTM as approxi-
mate information.
The matching uses feature based techniques. Point features are
extracted of the entire images using the Forstner operator. The
images of all sensors are matched pairwise in all combinations
using the cross correlation coefficient as similarity
measure. The results of pixel correlations are sets of image co-
ordinates (coordinate-pairs) of tie points for each image. In ad-
dition, the results are refined step by step through different levels
of image pyramids.
3.2 Mathematical Model of bundle adjustment
In the bundle adjustment the concept of orientation images pro-
posed by (Hofmann et al., 1982) is used. This approach estimates
the parameters of the exterior orientation only at a few selected
image-lines, at the so-called orientation images.
The mathematical model for photogrammtric point determination
with a three-line camera is based on the well known collinearity
equations. These equations describe the fundamental geometri-
cal condition that the rays through the three corresponding image
points and the corresponding perspective centers intersect in the
object point (see Fig. 5).
Two collinearity equations (Equation (1)) are established for each
image point. For every object point there are several equations,
because corresponding image points are found in images of dif-
ferent sensors.
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Figure 5: Imaging principle with three line camera
$;-—c fu - Xo) + fai (Y; T Yo) + 73) (Zi = Zo)
fia (Xs = Xo) + Fos (Yi EC Yo) zd fa3(Zi = Zo)
ly F12( Xi — Xo) + Pa2(Yı — Yo) + P3a(Zi — Zo)
: fia (Xi — Xo) t f33(Yi — Yo) + f33(Zi — Zo)
Ti: Yi : image coordinates of object point P
calibrated focal length
coordinates of object point P
0 : coordinates of projective center
43 : elements of rotation matrix
The collinearity equations are not in linear form and must be lin-
earized by a truncated Taylor’s expansion. Therefore, approxi-
mations for the orientation parameters and the object points are
required in bundle adjustment. All observations are used in a si-
multaneous least squares adjustment to estimate the unknowns.
There are two groups of unknowns, the exterior orientation pa-
rameters at few orientation points and the coordinates of the ob-
ject points. Furthermore, the observations are the image coordi-
nates of object points. The reduced normal equations containing
only the unknown exterior orientation parameters shows a band
structure. Because of the non-linearity of the problem, several
iteration steps are necessary.
3.3 Control Information in bundle adjustment
Starting point of this discussion about DTM data as control in-
formation is the approach of (Strunz, 1993). This approach de
scribes the use of DTM as additional or exclusive control infor-
mation for acrial triangulation. (Strunz, 1993) investigates the
conditions for datum determination by exclusive use of DTM. Fi-
nally, by means of simulations they analyse the accuracy achiev-
able with DTM as control information which don’t have to be
identified in the images. Transferring this approach to the case
of Mars Express and HRSC means that, the control information
is the surface defined by MOLA DTM and HRSC points lie on
these surfaces (Spiegel et al., 2003). A drawback of this approach
is that it does not use the original MOLA track points but interpo-
lated DTM points. The advantage of this approach is that the ef-
fort to search for adequate neighboring MOLA points is reduced
because the DTM has a regular grid structure.
Another approach is presented by (Ebner and Ohlhof, 1994),
which describes a point determination without classical GCPs,
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