ntation in 
described 
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ear image 
orphology 
se a small 
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lation and 
1age. The 
It shrinks 
the gaps 
  
minimum 
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od of each 
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ons of the 
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\R dataset 
An upper 
data. As it 
es are not 
re stressed 
(Notice the holes in the river surface). Further explanations 
about this method can be found in Killian et al. 1996. 
  
Figure 7. Original data (upper half) and result of filtering by 
morphological opening (lower half) — in river 
scenery (Briese et. al 2000) 
2.5 DUAL rank filtering 
Therefore, Eckstein propose a new filter, which does not use 
extreme-values, but a rank value instead. Rank operator R(p,r) 
is quite simple. It sorts all values p selected by means of 
structuring element, and chose one with a given rank value r. 
The values are ascending ordered, so if we choose first element 
(i.e. rank value is set to one), we get a minimum filter or with 
other words a morphological erosion. On the same way the 
setting the rank-value to last element in the ordered list results 
with morphological dilation. If rank-value is equal to n/2 the 
result is well-known median filter. Otherwise, if we set the rank 
value not equal, but close to 1 or n, we get morphological 
erosion or dilation much less sensitive to noise. Dual rank is 
defined as (Eckstein and Munkelt 1995): 
DR(p,r)  R(p,r)o R(p,n -r) 
Q) 
where DR(p,r) is dual rank operator, R(p,r) — rank operator 
p — pixel value, n — number of pixels selected by structuring 
element, r — rank value, o — stands for successive operations 
Dual rank consists of two successive rank operators, where the 
first one is set by given rank value r and second one uses 
complementary value n-r. This configuration allows a smooth 
and uninterrupted change of filtering characteristic from 
morphological opening to morphological closing by means of 
simple change of rank value from 1 to n. 
For optimal result in filtering off-terrain points, two parameters 
have to be given in the right way. 
a) rank-value 
b) dimension of structuring element 
As well as by iterative robust interpolation with linear 
prediction, these parameters are optimal for areas with similar 
morphometric characteristic only. Therefore, a progressive 
morphological filter for removing non-ground measurements 
from topographic LIDAR data is developed. 
2.6 Slope based filtering 
The basic idea is based on assumption that a large height 
difference between two nearby points is unlikely to be caused 
by a steep slope in terrain. So, this method takes into 
consideration a height difference between neighbored points, 
according their distance. A complete description with examples 
will be found in (Vosselman 2000). 
3. CHOOSING AN FILTER METHOD 
The geomorphologic characteristic of terrain together with 
distribution and morphometric characteristic of objects above 
them are most crucial to choose an appropriate filter method. 
The several basic cases may occur: 
- There is no vegetation or other objects present above 
terrain surface, or if so, they have such structure and 
size that they can be removed during the scanning 
process easily (areas with sporadic or without 
vegetation and without man made objects at all, i.e. 
karst, areas of excessive erosion, deserts, water 
surfaces..). All captured points belongs to terrain 
surface and their discrepancies from true surface are 
distributed normally, if there are no systematic errors 
present. In this case is reasonable to use the well- 
known statistical methods for detection and 
elimination of gross-errors (i.e. robust estimation) as 
well as the interpolation methods that are capable to 
remove the impact of random errors on the 
interpolated DTM (i.e. linear prediction). 
- The off-terrain points are present inside the dataset. 
There can be a lot of such measurements, often even 
more than terrain points, but they are spread over a 
whole dataset. This situation may occur at scanning of 
wooded areas, small villages. The plenty of filtering 
methods are developed for managing this situation 
(i.e. iterative robust interpolation with linear 
prediction, dual rank filtering, slope based filtering, 
3 
- The off-terrain points inside the dataset are not spread 
over a whole dataset, but they are grouped locally. 
This occasion can occur by scanning of large 
buildings in urban areas and by areas with very dense 
vegetation (i.e. rain forest), where laser beam cannot 
reach the ground locally. Some of above-mentioned 
methods are adopted to overcome this problem. 
However, the reality is mixture of all above-mentioned cases 
with their optimal filtering methods. Therefore, progressive 
filtering methods are developed.