. Istanbul 2004
Viti
Grid
grid cell (à, j)
n following the
r points, which
imation is per-
oints classified
iss
ergy functional
th the expected
he data term is
f local minima.
ie minimum of
[5 (4)
algorithm (Li,
minimum. In
The grid nodes
node, the cost
values the sur-
he value which
eated as attrac-
) of Sn by
) exists,
(5)
ual surface Sn
^J Within the
r the following
, < Nmax
(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 ) *
T J / (ij) TZ)
(5) = {es ) 2
> 9 on
Oy? [5 0zÓy / (5,
(7)
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