In: Paparoditis N., Pierrot-Deseilligny M.. Mallet C.. Tournaire O. (Eds), IAPRS. Vol. XXXVIII. Part ЗА - Saint-Mandé, France. September 1-3, 2010 
128 
extraction, features of a certain point are computed by using its 
neighbours within a spherical space with a fixed radius from the 
point. Thus, the following 21 features are extracted per each 
voxel and point. Figure 1 includes the colorized map of the 
ground truth and several important features derived by the 
point-based feature extraction approach. 
(b) Height 
(c) Vegetation echo 
(d) Sphericity 
(g) Homogeneity of surface 
normal 
(h) Density ratio 
(i) Hough Transformation 
(HT) 
(j) Point density 
Figure 1. Ground truth and 9 important features (blue: low and 
red: high) 
3.3.1 Height from ground level 
A digital terrain model (DTM) is formed by the recursive TIN 
fragmentation in every downward and upward stage (Sohn and 
Dowman, 2002). The height is the vertical distance from a 
certain point to the previously formed terrain surface in both 
approaches. If the terrain is one of the target classes whose 
classification is necessary, this would be the most important 
feature. 
3.3.2 Hough transformation (HT) 
The HT, which is a general method to extract linear objects such 
as roads from images, needs to be enhanced prior to being 
applied to the two dimensional points that are projected onto the 
base plane of each segment. This is because the projected power 
line points cannot be placed on an ideal straight line due to the 
system errors of ALS (the horizontal error with a laser scanner, 
the vibration of airplane, and GPS/IMU error) and 
environmental effects (ice and wind load). Additionally, 
multiple wires could exist within a segment. Therefore, for the 
HT value we consider a global maximum and several local 
maxima existing in the range near the 0 corresponding to the 
global maximum bin in an accumulating matrix of the HT 
domain. In here it is supposed that the multiple wires are 
parallel each other. When the perpendicular angle to the 
orientation direction of the line with the global maximum is 
e„ 
the range of 0 gmax -l to 6gmax + l is taken into account to 
find local maxima bins. The 0 size of a bin is 2 degrees, so the 
range for local maxima search is 0^* ±2°. Conclusively, the 
HT value considering the votes of a global maximum and local 
maxima is defined by: 
AL 
V + 
g max 
¿шшА / Г 
HT = 
Np,* * max 
0) 
where, F gmax = the vote of a global maximum bin 
J'rthmax ~ the vote of the i th local maximum bin existing 
between 0 gmax ±l 
Vma X = the number of maxima bins 
Vp, = the number of points within a segment 
3.3.3 Eigenvalue-based 
The eigenvalues are computed from the covariance matrix 
between x, y, and z of 3D points. Supposed that the extracted 
eigenvalues are X b X 2 , and X 3 (Xj > X 2 > X 3 ), three variables 
might have different values according to following three cases: 
X.) « X 2 ~ X 3 for scattering points, Xj, X 2 » X 3 for points on 
surfaces, and Xj » X 2> X 3 for linear structures. On the basis of 
this principle, the following features on eigenvalues are defined 
(Chehata et al., 2009): 
Anisotropy, which is opposed to isotropy, means the 
homogeneity of point distribution in three arbitrary 
perpendicular axes. This feature is useful to separate anisotropic 
structures except for vegetation. 
Anisotropy = ——— 
(2) 
Linearity: This helps to detect linear structures similarly to the 
HT. However, the linearity on eigenvalues also shows high 
values at building edges as well as power-line. 
Linearity = ^ ^ 
(3) 
Planarity: Planar structures such as ground and building roofs 
could be extracted by this feature. 
Planaritiy = ——— 
(4) 
Sphericity: This indicates the magnitude of equally distributing 
in all three directions for points. Vegetation could be strong. 
Sphericity = ~ 
(5) 
3.3.4 Surface-based 
The plane-based features are measured by generating an 
estimated plane or TIN models from member points of a given 
segment. These are associated with surface slope, surface 
roughness and homogeneity of surface normal. 
Plane slope: This is the angle difference between normal vector 
of an estimated plane and the z direction. The neighbouring 
points are regressed by a plane. Building roofs and ground 
mostly have weak values compared that vegetation has random 
values.