ted to the complexity of the distortion or the degree 
of necessary abstraction in the individual level. Of 
course a common theoretical framework for the algo- 
rithms in the different levels is of great advantage 
for the evaluation of the whole procedure. 
In our case, we have two different matching algorithms at 
hand, which are suited for measuring smooth surfaces: 
1.) The least squares matching (LSM) (Pertl 1984) algo- 
rithm leads to the highest possible accuracy, as it 
exploits the precision inherent in the image data as 
far as possible. Typical standard deviations lie in a 
range between 1/20 and 1/5 of a pixel, or 1 - 4 um if 
a pixel size of 20 um is used. The algorithm is able 
to estimate terrain heights and slopes, if the tex- 
ture within the window allows it. Typical computing 
times on the A900 computer are 2 - 3 seconds per 
point if a window size of 12 x 12 is used. Main dis- 
advantage of this matching algorithm is the small 
pull-in range of 2 - 3 pixels or 20 - 40 um resp.. 
2.) The feature based matching (FBM) algorithm (Fórstner 
1986) can provide approximate values of at least this 
quality, starting from a window of up to 128 x 128 
pixels. The algorithm results in a list of typically 
20 - 50 selected points with their heights, i. e. 
parallaxes and an estimate for the average slope 
within the window. These points can further be pro- 
cessed using LSM taking the estimated heights and 
slopes of the FBM as approximations. The standard 
deviations of the parallaxes from FBM typically lie 
in a range of 1/2 and 2 pixels. For reasons of com- 
puting time and core memory requirements on the A900 
we operate with 40 x 40 windows for which the 
matching time is 3 - 4 seconds. The pull-in range is 
about 10 - 15 pixels or 0.2 mm - 0.3 mm in the image. 
The disadvatage of this algorithm is the still too 
limited pull-in range with respect to rotations, 
scale differences and shears (cf. above). 
If one wants to use the two matching algorithms to build 
up a hierarchy which also exploits the full area of the 
digitized image patch of 256 x 240 pixels, say, one arrives 
at the five level hierarchy for the whole measuring proce- 
dure, which is shown in table 1. 
The sequence of levels is chosen in a way that the 
pull-in range in one level is appr. two times the standard 
deviation (precision) of the next higher level. The levels 3 
and 4 desribe the already existing hierarchy of the manual 
measurement procedure including preparation (level 4) and 
actual measurement (level 3). 
= 611:* 
OE dec 
  
E 
es 
ms. 
3