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(3) can be rewritten as a system of observation equations 
and represents the functional dependence between the 
independent unknowns Zi; and pum,» and the optimizing 
criterion. So far there exists no fundamental difference 
to the frame image approach, but there is one difficulty: 
H» can't be expressed explicitly (see chapter 2.1). It is 
only given implicitly and must be calculated iteratively. 
Control information is added to (3) and the unknowns 
are solved for using the standard least squares formulae. 
3.3 Initial values using a hierarchical approach 
Non linear least squares adjustment needs initial values 
for the unknowns to start with. In image matching hier- 
archical procedures /Burt, Adelson 1983/ from coarse to 
fine have been used to provide them /eg Li 1989/. An 
image pyramid as well as a DTM pyramid are generated 
from level 0 (the original image and the DTM). For the 
next higher level 2*2 elements are combined into one 
element, thus the resolution is coarser by a factor of 2 
and the amount of data by a factor of 4. In this way several 
levels are computed. 
The adjustment process starts with some coarse initial 
height values (ideally a constant value) in the highest 
level of the image and DTM pyramid. In every level the 
iteration proceeds until an end condition is reached. 
Then the DTM values of the next lower level are calcu- 
lated, eg by linear interpolation, and the computation 
proceeds on that level, until level 0 is processed. 
4. CONDUCTED EXPERIMENTS 
Real data from high resolution 3-line cameras with 
known flight path are not yet available. Therefore, the 
algorithm was tested with simulated data. The main goal 
of the simulations was to investigate the influence of 
white noise in the grey values and of random errors in 
the exterior orientation onto the matching results. 
4.1 Input data 
For the simulations we produced so called semi-synthe- 
tic image strips. We used a real orthoimage from the 
" Vernagtferner', a glacier in Austrian Alps /Rentsch 
1992/ together with the corresponding DTM and gene- 
rated three image strips by means of inverse orthopro- 
jection. We used orientation parameters corresponding 
to a straight flight path with constant velocity. The simu- 
lation parameters were chosen as follows: 
Ground elevation: 2620 m - 2950 m 
DTM mesh size: 50m*50m 
Object surface element size: 3.125 m * 3.125 m 
(eg 16 * 16 object surface elements per DTM mesh) 
Flight altitude: 300 km 
Speed: 7700 m/s 
Sensor pixel size: 10.4 um 
Sensor read out frequency: 2464 Hz 
Radiometric resolution: 8 bit 
Convergency angles: 2 x 20 grad 
Calibrated focal length: 1.0m 
The used DTM can be seen in figure 4.1. In figure 4.2 the 
semi-synthetic image strip for the nadir looking sensor 
(1024 * 1024 pixels) is shown. The central part consisting 
of 256 * 256 pixels was used in the simulations. The image 
texture in this area is rather good. 
Radiometric noise with different standard deviations 
was added to the grey values of all image strips. o. = 3.0 
grey values corresponds to a well calibrated CCD sen- 
sor, or = 12.0 to the noise, which must be expected in 
digitized films /Diehl 1990/. In the case of or = 0.0 no 
noise was introduced. However, the generation of the 
image strips inherently induces quantization noise and 
interpolation errors. 
  
Fig 4.1 The Vernagtferner DTM used for the 
simulations