The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
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Figure 2. GRASS and TopScan terrain points in the buildings 
mask. The error is close to the building edge and so it is 
probably due to the mask itself. 
3. DTM/DSM RELATIVE CONTROL 
3.1 Creation of gridded products with GRASS 
Starting from the points classified as terrain by GRASS it is 
possible to compute the DTM. The used procedure (another 
GRASS algorithm performed by us and called v.surf.bspline, 
still free available in GRASS) executes the interpolation of 
sparse points on a regular grid using bilinear or bicubic splines. 
The DSM instead can be performed with a simple interpolation 
of the first pulses, without a preliminary filtering procedure. 
Splines interpolation requires as input the spatial resolution, 
which corresponds to the splines number that will be used. A 
large number of splines implicates an increment of the number 
of unknowns and problems related to the irregular behaviour in 
correspondence of zones with a lack of data. Another problem 
related to use a high resolution is the possibility to have a 
number of unknowns larger than the number of equation: the 
spline coefficients cannot be estimated. A low resolution instead 
implicates a surface that does not follow the data trend where 
the points have a high variability. 
The density of the raw data is 1 point/m 2 , so we choose a spatial 
resolution of the splines equal to 4 m to avoid problems related 
to the lack of data and the increment of the computational cost. 
In 2 areas (with a surface of 3.01 and 6.58 km 2 respectively) a 
DTM and a DSM were performed with a resolution of 2 m. 
3.2 Relative control 
A grid model can be intended as a raster. This means that it is 
possible to operate with grid model using algebra raster 
procedures. The basic idea is to compare Sardinia and GRASS 
gridded products with a raster difference and obtaining a new 
raster map. The results related to the DTMs map difference are 
shown in table 3. 
Area 
S (km 2 ) 
mean (m) 
std (m) 
min (m) 
max (m) 
B 
3,011 
-0,11 
0,35 
-4,79 
3,02 
C 
6,58 
-0,08 
0,27 
-3,88 
1,69 
Table 3. Differences between Sardinia and GRASS DTMs 
The average of the difference is about -0.1 m and the standard 
deviation results lower than 0.4 m. The spatial resolution of the 
DTM makes the error irrelevant and probably caused by the 
presence of particular situations (as indicated also by the 
minimum and maximum values). 
A more detailed control about the error size indicated that the 
major part of the errors (over 95%) has a value lower than 1 m. 
This analysis was performed by using some thresholds value 
(0.5, 1, 2, 3 m) and verifying the number of elements which 
belong to the fixed threshold. Results are shown in table 4, 
where it is possible to observe that the points with an error 
larger than 3 m are an irrelevant percentage. 
Area 
• < 0,5 
0,5 < • < 1 
1 <*<2 
2 < • < 3 
• > 3 
B 
90,73% 
6,82% 
2,03% 
0,35% 
0,07% 
C 
93,81% 
4,80% 
1,22% 
0,16% 
0,01% 
Table 4. Distribution of the DTM error 
(threshold values in meters) 
In any case, another control was performed to discover the 
causes of the difference where there are significant 
discrepancies. The map of the difference was superimposed on a 
high quality orthophoto (resolution 0.125 m) and then a legend 
about the difference was associated. This process allowed us to 
find the zones where the discrepancies assumed the largest 
values. 
This control demonstrated that the larger differences are located 
close to particular elements like big rocks, wharfs, foundations, 
pools et cetera. 
The reflection given by a big rock is similar to the reflection of 
a building. Thus, a big rock can be interpreted by GRASS as a 
building and so removed. Sardinia’s classification instead 
includes also this kind of elements, and during the manual 
correction it is possible to distinguish a rock with respect to a 
building. In figure 3 the differences between Sardinia and 
GRASS DTMs are shown, and they assume a positive value 
where there is a rock, which confirms the previous hypothesis. 
In any case, in our opinion, only with a manual control it is 
possible to take account of these anomalous situations. 
Figure 3. Typical element which causes misclassification 
Another interesting case is the presence of wharfs (figure 4). 
The automatic algorithm classifies a wharf like a logical 
continuation of the terrain because these elements have a height 
almost equal to the terrain. It is possible to observe that others 
objects (e.g. motorboats) and the undeep water have the same 
problems.