The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
roof planes and hence the intensity values are higher for the 
eastern planes and lower for the west ones. 
3.2 Point Density 
The calculation of the incidence angle and the planarity is based 
on the determination of the covariance for each point by 
including all neighbour points inside a sphere with predefined 
radius. For a radius of lm we may get about 30.5 points as 
average, if we include all flights. Flight 3 delivers as average 
only 8.8 points. Increasing the radius by factor 2 we get the 
average value of 120.6 points per sphere and all flights included, 
where 33.6 points are originated from flight 3. Due to the small 
size of the roof regions we select a radius of lm to avoid too 
much disturbance for the points near the border of the object 
planes. The inhomogeneous and anisotropic point distribution 
causes a reduction of the planarity value and raises its standard 
deviation even if the 3rd eigenvalue equals to zero, because the 
eigenvalues belonging to both eigenvectors parallel to the plane 
may differ, as discussed by Gross (2006). Investigations 
concerning the quality of the point position are also presented 
by Bae et al. (2005). 
4. SELECTION OF HOMOGENEOUS REGIONS 
For the assessment of the adapted intensity / we prefer regions 
with different orientations but homogenous surface reflectance 
to separate the influences of the incidence angle and material 
effects. The roof planes within our scene cover a large band of 
possible incidence angles but most of them have same tiles. The 
selected regions contain the same material but varying angle vs. 
flight direction and the direction of the laser beam. Each roof 
plane is labeled by a region number. 
region number region number 
a b 
Figure 5. Angles [°] of flight 3 for all selected plane regions 
sorted by the mean angle together with its standard deviation: a) 
slope of roofs, b) incidence angles. 
This selection includes a wide range concerning the off nadir 
angle for the laser beam. The variation inside the regions is 
small because the regions are small in comparison with the 
distance to the sensor. The slope angle of the roof planes ( 
Figure 5a) encloses a few nearly flat roofs but also steeper roofs 
up to 50°. For each point of the point cloud inside the region the 
slope angle is calculated based on the eigenvector of the 
smallest eigenvalue. Therefore the data set encloses regions 
with small and height variations of the slope angle, which may 
be influenced by small objects on top of the roofs.The planarity 
yields high values for planes objects, where the mean value 
varies from 0.67 to 0.83. Due to noise and disturbing small 
object parts, higher values could not be achieved. The standard 
deviation inside the regions varies from 0,06 to 0.13, which 
indicates, that the planes are not exactly planar and does not 
show the same roughness. The incidence angle ( 
Figure 5b) varies from 2° to 68° with a mean value from 44°. 
The standard deviation delivers values from 0.5° to 12° with a 
mean value from 4°. Inside a region the variation of the 
incidence angle is small. The distances R between sensor and 
object surface varies from 429m to 449m with a mean standard 
deviation of lm. 
5. RESULTS 
For the selected regions the given intensity is normalized by 
division with the cosine of the incidence angle. By this division 
the normalized intensity value increases compared to the 
original one. Therefore we use the mean value /u(x) and the 
standard deviation cr(x) for the calculation of the variation 
coefficient V c (x) = cr(x)/p(x) . This coefficient is scale 
invariant and regards the dependency of the standard deviation 
from the intensity as presented by Pfeifer et al. (2007). 
5.1 Global Consideration Over all Regions in Common 
Mean value and standard deviation of the variation coefficient 
over all roof regions with nearly the same material 
p(V c ( region ) ) and a ( V c ( region ) ) 
are determined and written in 
Table 1. Considering only flight 3 or 4 there are no significant 
value modifications, but including flight 3 and 4 together the 
normalization delivers an essentially smaller standard deviation. 
The variance of the incidence angle for each region increases, if 
data from more than one flight are used. In the last column of 
Table 1 we see the corresponding values by regarding all flights. 
In this case we get a good improvement for the normalized 
intensity. 
Flights 
3 
4 
3-4 
1-7 
before 
normali 
zation 
MKÏ 
0.145 
0.142 
0.162 
0.189 
a ( V c) ■ 
0.030 
0.027 
0.028 
0.039 
after 
normali 
zation 
M(r c ) 
0.145 
0.144 
0.150 
0.161 
A v c) 
0.027 
0.023 
0.023 
0.023 
Table 1. Mean value and standard deviation for different flight 
situation data sets before and after normalization. 
5.2 Consideration of each region separately 
For an assessment the ratio of the variation coefficient 
R v (region) = V c after (region) ¡V cbefore (region) for all 
selected regions after vs. regions before normalization are 
calculated. The sorted ratios are drawn in Figure 6. 
408