The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
410 
Best power for each region 
0 0.5 1 1.5 
power of cosine 
Figure 9. Best values for the power of the cosine. 
This figure shows the number of regions among the selected 
ones together with its power delivering the smallest coefficient. 
For p = 0.75 we get a common minimum for all regions 
meaning the sum of the variation coefficient over all regions is 
minimal for this power. This power may depend on the material. 
6. DISCUSSION AND CONCLUSION 
The measured LIDAR intensity values depend on the distance 
between sensor and object as well as for the incidence angle 
defined by the beam direction and the normal vector of an 
object surface. The normalization of the intensity by 
considering the object distance in a typical urban area yields 
only small modifications below 5%. Larger effects on the 
intensity are caused by the incidence angle. 
Investigations on full-waveform laser data are realized, where 
for each measured point of the point cloud the amplitude and 
width values are available. In a first step the range modified 
intensity, influenced by the distance between sensor and object 
surface, concerning the geometry and the extinction of the 
signal is evaluated. In a second step we divide the new intensity 
value by cosine of the incidence angle following the 
Lambertian law. 
All processing steps are done on aerial laser elevation data of a 
urban area including differences in the distance and a large 
interval for the incidence angle, especially if we include more 
than only a single flight. Including all flight we get about 9.6 
points/m 2 . The distribution of the points implies high variances 
for the locally calculated planarity even if all points fall in a 
plane. 
For assessment of the normalized intensity values we have 
selected nearly homogenous regions interactively. The variation 
coefficient is selected as measure for the comparison of the 
values before and after normalization. Mean and standard 
deviation of this measure over all regions decreases by the 
normalization, especially if all flight are included. For about 
75% of the regions we get better values, for the other region we 
may have disturbances on the roofs like a chimney. The same 
process is evaluated also for streets parts but is not discussed 
here. A detailed discussion of the intensity behaviour inside a 
region demonstrates a high variance even for constant incidence 
angle. This may caused by material features or local surface 
effects. Nevertheless normalization in common with the 
Lambertian law is useful. A modification of this law can 
produce a better result with respect to the variation coefficient 
and for the situations used her. There is no extrapolation test for 
other material available as yet. 
Removing well known influences on the intensity value 
separates different effects and supports the understanding of the 
data for further analysis. 
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