The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
Figure 5. Typical case of points on a buildings (black spots) 
Firstly the control points were rasterized with a resolution of 0.2 
m and then the differences were calculated. The mean was 1.45 
m and the standard deviation 2.87 m, the maximum difference 
was larger than 7 m. These results are due to the position of the 
points and, as previously said, they generally lie close to the 
edge of the buildings and so the differences can be calculated by 
using the cells which have the height of the terrain or a 
intermediate value between the terrain and building heights. 
To avoid this problem the difference were manually calculated 
in order to chose the exactly cells. The new results indicated a 
mean of 0.22 m and standard deviation of 0.73 m, that are 
acceptable values. 
5. ALGORITHM PERFORMANCE 
As previously described, the algorithm is composed of three 
sub-functions but the computational cost is primary due to the 
first one: the edge detection phase. The necessary time to 
complete this step depends on the fixed splines resolution. To 
halve the splines step means to increment the number of splines 
by four times (and obviously also the number of unknowns). 
Therefore it is obvious that the choice of an appropriate number 
of splines depends on the density of the raw data and on the 
accuracy of the final products. While we can suggest a default 
set of parameters that we consider adequate for many situations, 
the choice of the spline resolution must be made always 
considering what the users wants to obtain. The unique general 
rule we suggest is to use a spline step larger than the mean 
density of the original spread data. 
The last function that composes the algorithm still requires the 
splines step as input parameter, but in this case we suggest to 
use the default parameter (60 m), because the interpolated 
surface in this case must be smooth. In fact only a control with a 
smooth surface is necessary in order to detect misclassification 
errors. 
The performances of the algorithm were evaluated with the 
analysis of the results as a function of the splines resolution. 
The test was performed in an area of 6.58 km 2 , with a splines 
step variable from 4 to 32, passing through the multiple of 2. 
The used computer has a processor Core Duo T5500 and 2 GB. 
The necessary time during any test was appointed and the 
results are shown in figure 6. 
32m 16m 8m 4m 
spline resolution 
Figure 6. Time as a function of the spline resolution 
The main part of the computational cost is given by the edge 
detection step. In fact it depends on the spline resolution. The 
necessary time has a value of some hours when the resolution is 
very high; instead when a low resolution is fixed it is necessary 
to wait only for few minutes. The other two commands have a 
computational time constant during the different elaborations. 
The accuracy of the new DTMs can be again estimated using a 
comparison with the Sardinia’s DTM and the points measured 
with the GPS (see table 7). It is obvious that a large step 
generates a not so much accurate DTM (e.g. when the resolution 
is 32 m the mean error is 0.59 m and the root mean square error 
is 1.2 m). In any case, when a low resolution DTM is required, 
it is possible to compute it in few minutes (less than 30) because 
the error committed is always smaller than 1.5 m. On the 
opposite, when we need a better accuracy (e.g. mean error less 
than 0.35 m and root mean square less than 0.39 m in our case), 
more detailed splines are required and so more computing time 
(several hours). 
splines step (m) 
Sardinia minus GRASS DTM (m) 
mean 
std 
max 
min 
4 
-0,11 
0,35 
3,02 
-4,79 
8 
-0,05 
0,31 
4,43 
-3,62 
16 
0,04 
0,38 
5,47 
-3,62 
32 
-0,05 
0,49 
5,55 
-3,47 
GPS minus GRASS DTM (m) 
mean 
std 
max 
min 
4 
0,36 
0,16 
0,73 
-0,19 
8 
0,56 
0,43 
1,74 
-0,41 
16 
0,66 
0,5 
1,96 
-0,06 
32 
0,91 
0,68 
2,53 
0,03 
Table 7. Results as a function of the splines resolution 
6. CONLUSIONS 
An algorithm to filter LiDAR raw data and several controls 
about the obtainable results were presented. The algorithm is 
completely free and already available on Internet 
(http://grass.itc.it). The possibility of having such a kind of 
algorithm completely integrated within a GIS (GRASS), its 
filtering performances (here presented) also in fully automatic 
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