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Peter Lohmann 
  
use of intensity-images, which can be produced by some of the laser scanning systems, or the combined use of first- and 
last-pulse data and supporting GIS data or video was of help to improve the process of filtering. 
This paper discusses the automatic derivation of the terrain-surfaces from Laser-DSM, without the use of additional 
information. Two filter approaches discussed in detail namely the frequently used method of "linear prediction" 
(Krauset al. 1997, Lohmann et al.1999) and of morphological image processing, in the form of the "Dual-Rank-Filter" 
(Eckstein et al. 1995, Schaeffer 1999). 
2 DATA SET USED 
Data acquisition for the experiment described in this paper was carried out by the company "TopoSys Topographische 
Systemdaten GmbH" in March as well as April 1998, using their laser-scanner-system (Lohr et al., 1995). The test-area 
is located in the west of Germany in the state North Rhine-Westphalia a few kilometers north of Recklinghausen. This 
is an area which is heavily influenced by coal mining and terrain subsidence. Under the responsibility of the "Deutsche 
Steinkohle AG" (DSK) the company TopoSys was contracted to perform a laser scanner survey. The TopoSys-Sensor 
works with help of a fiber glass bundle. The across-track resolution at a field of view of +7° is 127 points within each 
scan. This means, the spacing between two fibers amounts to 0,11?, which corresponds to a point-spacing of 1,73 mat 
a cruising altitude of 900 m. In flight direction, a spacing between two scans ranges from 0,11 to 0,13 mat a speed of 
70-80 m/s . A point density of 4 to 5 samples per m? is thus achieved . 
3 LINEAR PREDICTION 
The linear prediction is a statistical interpolation-method, being particularly suitable to the interpolation of digital 
terrain or surface models. The height-values to be filtered are available in irregular form or are arranged in a raster. A 
detailled description of the basics for this method can be found in (Kraus, 1997, Lohmann et al., 1999, Koch, 1999). In 
the following the implementation within the software DTMCOR at the Institute for Photogrammetry and Engineering 
Surveys at the University of Hanover is shortly described. 
The linear prediction is based on the correlation of neighbouring points, expressed in the covariance function. In 
DTMCOR it has the form: 
-1,30103 [2j 
C(PP,)=C(0)-e (1) 
The covariance between two points P; and P; depends on their spacing PF; (Figure 1). If the points are close to each 
other, the covariance is high. With growing distance, the covariance tends against zero. C(0) is the vertex-value of the 
covariance function, the covariance for the 
  
spacing zero. In DTMCOR it is restricted to 
0.99. B describes the distance, in which the 
Figure 1: : Te 
à a der effect of the covariance function is reduced to 
25%. The value —1,30103 is a constant factor, 
function 
C(0) and B are parameters, that are defined in 
the dialogue between the software and the 
user. 
In order to perform linear prediction, it is 
neccessary to first separate a trend function. 
This can be done by means of a polynomial of 
very low degree or a moving plane. The result 
is the vector z which contains the centered 
  
  
  
  
points of measurements z; These values 
  
describe the deviations of the sample points 
from the trend function. Trend separation within DTMCOR is performed by the calculation of a moving plane, which is 
defined by three unknown coefficients ay, a;, a». 
Z; = ao + a; X; * a» Y, (2) 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 541