In: Paparoditis N., Pierrot-Deseilligny M.. Mallet C. Tournaire O. (Eds). 1APRS. Vol. XXXV1I1. Part ЗА - Saint-Mandé, France. September 1-3. 2010 
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Homogeneity of surface normal: TIN generation is first 
necessity to create a surface model. This feature is the variance 
between the normal vectors of TINs. Vegetation has very high 
value in the variable. 
Surface roughness: This feature is the root mean square of the 
orthogonal distance from points to an estimated plane. 
Vegetation would stand out since its point dispersion. 
Distance to surface: This is closely similar to the surface 
roughness, but is the vertical distance between individual point 
and an estimated plane. 
3-3.5 Convex hull-based 
XY projection area: For this feature, the member points are 
projected on XY-plane, and then the convex hull of the 2 
dimensional points is run to derive their boundary. XY 
projection area is area of the region formed by the 2D convex 
hull. Ground and building roof could have high value of the area. 
On the contrary, power-line has almost zero value. 
Bounding volume: Through computing the 3D convex hull of 
member points, the bounding volume of the polyhedron shaped 
by the points can be estimated. Unlike the XY projection area, 
bounding volume might be strong in only case of vegetation. 
3.3.6 Echo-based 
Echo-based features are determined by combining the number 
of points corresponding to single (N s ), first (Nj), intermediate 
(Nj), and last return (N/). N pt is the number of all member points. 
In here, the single return indicates a unique reflection without 
multiple returns, and the first return means the first reflection 
among multiple returns. 
Terrain echo: Although terrain points are not importantly dealt 
with in this study, this feature would be helpful to roughly 
classify raw data including terrain. Terrain is mainly recorded as 
single return or last return. Therefore, the two returns are 
considered for terrain echo. 
TerrainEcho - 
N , 
(6) 
Vegetation echo: The efficiency of this feature has been 
already validated by Rutzinger et al. (2008) for urban vegetation 
classification. Generally, vegetation has a considerable amount 
of intermediate returns due to multi-return from its leaves. In 
addition, the first return would be found on crown surface of 
vegetation. Consequently, vegetation mostly has the 
intermediate return and the first return in LIDAR. 
N f + V,. 
VegetationEcho = —- 
N„, (7) 
Power-line echo: Power-line structure should be constructed on 
an open place which is not surrounded with any natural or 
artificial obstacles dangerous enough to break down it or where 
the obstacles have been removed by human. Accordingly, a 
laser pulse hitting a power-line has mainly a first return 
reflected from the power-line. Furthermore, the foot print size 
of the laser which approaches a power-line is bigger than the 
diameter of the power-line. That is, there would be another 
return from typically ground. Therefore, power-line is generally 
first return among the multiple returns, not single return. 
PowerlineEcho = 
N, 
N.. 
(8) 
Building echo: A laser cannot surely penetrate building roofs 
made of the concrete materials. In other words, there is no more 
return excluding a reflection from roofed top. Building echo 
considering only single return is defined as follow: 
N 
BuildingEcho = —— 
N , 
(9) 
3.3.7 Density-based 
Point density: is the number of points within a given segment 
divided by its volume. Generally, these for ground and building 
roof are the largest and vegetation is stronger than power-line in 
the value. 
Density ratio: This feature was also invented by Rutzinger et al. 
(2008) to differentiate vegetation. According to his method as 
shown in figure 2(a), density ratio of a certain LIDAR point 
means a ratio between point densities of a projected circle from 
a cylinder of radius r and a sphere of radius r (Eq. 10). This 
method is applied for point-based approach. However, for 
voxel-based approach, this is rearranged by considering a cube 
and a rectangle instead of a sphere and a circle as the figure 2(b). 
It is defined as Eq. 11. 
DR, 
DR, 
N, 
N 2D 
_n 3D 
4 r 
1 
N,r, D w 
(10) 
(И) 
where, N 3D and N 2D are the number of points within a target 
segment (sphere or voxel) and the projected shape (circle or 
rectangle) respectively. The r and D v indicate radius of a sphere 
and the voxel size. The overhead and separated power-lines 
have low values because of plenty of ground points under it. It 
is very high in case of objects with dense points around such as 
ground and building. Vegetation would be between power-line 
and ground. 
(a) Point-based computation (b) Voxel-based computation 
Figure 2. 3D/2D density ratio 
3.3.8 Vertical Profile 
Vertical structures such as trees, streetlights and power-line 
towers show the vertical continuity of on-segment, in here on- 
segment means the segment occupied with one or more points. 
In contrast, floating structures like power-line have a few of 
vacant segments called off-segment. For extraction of these 
features, a vertical profile (rectangular column for voxel-based 
or cylinder for point-based) is sliced by several bins of 75cm 
height (a quarter of segment size). 
On-segment: is the number of on-segments along to a vertical 
profile. 
Continuous on-segment: This feature value corresponds to the 
maximum count of on-segments stacked continuously. It is