tches 
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George Vosselman 
  
of type Il errors for this filter is larger than for the probabilistic filter. For both filters, the number of errors, in particular 
the number of type I! errors, becomes larger for thc datasets with a lower point density. In the probabilistic filter the 
maximum height differences were derived such that they minimise the number of errors. In table 1 the total amount of 
errors indeed appears to be smaller in case of the probabilistic filter. 
  
More important than the number of errors is 
  
  
  
  
  
  
A : 2 Point density Mean error RMS error Max. error 
the effect of these. errors onto the digital Inu 7 - T 
i * ; : s a (points/m ) max : prob max : prob | max ' prob 
elevation model. For this purpose the heights T 
wie al ts i 0.01 : 0.00 000 * 007 972 . 197 
of type II errors were interpolated in the TIN : : an one 
of the filtered reference points and the heights He el ; (0l 017 ; 21) 395 os 
à = 1/16 0.06 : 0.04 030 *. 022 422 5.320 
  
  
of the type I errors were interpolated in the 
TIN of the filter results of the reduced datasct. Table 2. Error size statistics (m) 
The statistics on the errors sizes are shown in 
table 2. Again the results of the probabilistic filter are better than the results of the maximum filter. Most classification 
“errors are relatively small. Therefore, the mean error remains quite small. The rool mean squarc error values clearly 
increase if the point density decreases. This is also illustrated in figure 4. In the DEM reconstructed from one point per 
16 m2 several height variations can be seen that are caused by unfiltered points in vegetation. Also the ditches (about 5 
m wide and 50 cm deep) can not longer be reconstructed. 
The maximum errors in this test became quite large, sometimes even larger than the maximum value in the filter 
functions. This is caused by points that had no other point within a distance of 10 m. Since this was the maximum range 
of the derived filter function, these kind of points could not be filtered. 
i55 SS 
        
     
us. A ut ER FE S £F Ca m s AN NS EN i. N ESS 
  
Figure 4. Original (left) and filtered (right) data in a perspective view. The images arc derived from the original data of 
5.6 points/m' (top) and the reduced data of 1 point / 16 m” (bottom). 
6 CONCLUSIONS 
In this paper a method has been presented for filtering laser altimetry data. The method is closely related to the erosion 
operator used in mathematical morphology. The shape of the filter function can be derived from a set of training data. Tt 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 941