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Viti 
  
  
  
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grid cell (à, j) 
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oints classified 
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ergy functional 
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f local minima. 
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algorithm (Li, 
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(6) 
Geocoded 
  
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004 
where óz is a constant and SI is the value of S,, at the (k — 1)th 
iteration of the process. 
(5,3) 
The regularization term E7eÿ ‘(Sn ) approximates the curve's ten- 
sion and the sum of the square of the curvatures 
5 68, V? 88, V? 26. V? 
EDS) ( 5 ) * ( 5 ) + (Z3 ) * 
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Partial derivatives are calculated using centered finite differences. 
4 THE DATA SETS 
This algorithm has been tested with various LIDAR systems. The 
scan mechanism of TopoSys is based on a fixed glass fiber array. 
Its specific design produces a push-broom measurement pattern 
on the ground. TopoSys data were acquired both from an air- 
plane and an helicopter vector. The data set over Roujan, South 
of France, corresponds to the last recorded pulse. The ground is 
more likely visible with this pulse. But the first echo was used 
over the city of Amiens (there was not any vegetation in the test 
area). On the contrary, the ALS40 works with a rotating mirror, 
providing an entirely different ground pattern. 
Table 1 gathers the main information about the different LIDAR 
data sets. 
  
  
  
  
  
  
  
  
  
| Test Area || Amiens | Roujan | Montmirail | 
Height (1) 1005 900 3000 
System TopoSys TopoSys ALS40 
Vector Plane Helicopter Plane 
Density (pt/m?) 75 26.8 0.07 
Landscape City rural mountain 
Extension 0.64 km” 0.2 km” 36.8 km” 
Nb of pts 3.10° 4.10° 4.10° 
  
  
  
  
  
  
  
Table 1: Overview of the test data sets 
Moreover, various landscapes (city centers, rural landscapes, 
forested and mountainous areas) were processed in order to have 
a large overview of the algorithm behavior. 
5 RESULTS 
The initial surface S;n was computed within a 3m x 3m grid size. 
Nevertheless, as mentioned before, we did refined the resolution 
applying a simple Nearest Neighborhood interpolator so that the 
final resolution should be 0.5 m. In order to make this surface 
twice differentiable, we did apply a weak gaussian filter before 
computing the energy minimization algorithm. Laser data over 
Roujan and Montmirail have been processed with a 15m x 15m 
square neighborhood, whereas we used a 20m x 20m square 
neighborhood for Amiens. œ was set up to I 
Figure 4 shows laser points (green) classified as non-ground 
points projected onto an aerial image acquired over the city of 
Amiens. The result of the classification clearly shows that within 
this dense urban area, all buildings have been detected as well as 
small inner courtyards. Since both laser and image surveys have 
not been acquired in the same time, mobile objects may not fit. 
Even if it is not depicted on the Figure 4 for readable concern, 
cars are classified as low non-ground points. 
  
Figure 4: Laser points (in green) classified as non-ground points 
projected onto an aerial image (20 cm resolution) over the city 
of Amiens, France. 
Figure 5 presents a 3D-view of a classified laser landscape over 
the area of Roujan. The high point density of this data set (26.8 
pt / m?) allows us to detect micro-relieves with a good accuracy. 
We can point out the regular pattern of the low non-ground class 
such is vineyard in this case. Small copse (red) have also been 
detected. White points belong to the ground. Even if the second 
laser echo has been used here, we may notice that ground is not 
seen everywhere on the scene: last pulse does not penetrate dense 
canopy. 
  
Figure 5: 3D view of a classified laser landscape over the area 
of Roujan, France. White, blue and red points are respectively 
ground,low non-ground and non-ground laser points. 
In order to have a more detailed description of the results, we 
present in Figure 6 a profile of both the final DTM (in gray) 
and the classified laser points over an other location of the Rou- 
jan data set. Low non-ground points (blue) are mainly vineyard 
whereas non-ground points (green) are vegetation. After 15 it- 
erations, the deformable model algorithm found the best surface 
(fitting our criteria). The calculated DTM (with a 0.5 n reso- 
lution) describes a relevant micro topography, even where laser 
points are missing. 
Figure 7 shows the prime terrain estimation Sin (black line) over 
the same profile as in Figure 6. The final DTM (gray lines) shows 
the refinement after the processing of the deformable model algo- 
rithm. 
The algorithm works with various laser data (see Table 1). Fig- 
ure 8 shows the resulting DTM of a large scale laser survey 
(36.8 km?) with a low point density over the mountainous area 
of Montmirail, South of France. What is of importance in this re- 
sult is the capability of the algorithm to compute a large amount