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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
Figure 6. Sorted ratios of the variation coefficients after vs. 
before normalization of the intensity. 
About 75% of the selected regions become values below 1.0 
meaning the new coefficient is better (smaller) than the 
previous one. In some cases with higher values than 1.0 the 
regions contain chimney and dormer windows. On the other 
side we can not be sure, that the borders of the regions are well 
defined inside a homogeneous area. 
Obviously the effect of intensity normalization is not as much 
evident for street regions. The variance of the incidence angle is 
much smaller than for roofs. 
5.4 Intensity of a region with different geometry 
For the investigation on the intensity within a region, we select 
two neighboured planes with the same material and the same 
gradient direction but varying roof slopes. The intensity values 
for all points inside this region are visualized in 
Figure 8 coloured by the flight number. 
Figure 8a shows the original data and the approximating cosine 
curve as black line. In b the normalized intensity values are 
scaled in such a way, that the mean value, drawn by a black line, 
remains the same as before. The correspondence between flight 
number and colour is depicted in top of 
Figure 8b. There exist no points from the flights 1 and 6. 
5.3 Visualization of the Normalized Data 
The intensity improvements are demonstrated by the following 
figures showing the intensity values before and after the 
normalization by the incidence angle. For comparison reasons 
the colours dark blue and dark red are bounded to the thresholds 
5% respectively 95% as lower and upper percentiles of the 
intensity. The normalized intensity reflects higher intensities 
without large variations for the roof planes but lower values for 
points near the ridge, where the planarity is not given. The 
results for a pyramidal roof including four planes are shown by 
Figure 4. The original data shows higher values for the south 
west planes than for the north-east ones caused by the flight 
paths and directions ( 
Figure 2). In the normalized data all four planes have same 
intensity values and appear homogeneous. A building 
composed by several parts with different orientation is given in 
Figure 7. The original data demonstrates again the dependency 
of the intensity from the incidence angle. By the normalization 
this dependency is compensated and again the intensity is 
adapted. 
Figure 7.Intensity data for different orientated roofs. 
Gabled roofs: a) original, b) normalized, Pyramidal roof: c) 
original, d) normalized. 
10 20 30 40 50 
incidence angle [°] 
t • • » * • « • 
c 5000 . • ... 
•— 4000 
"O 
<D 
3000—- 
CO 
§ 2000 
o 
1000, 
• i: ‘A . •« X vt; 
■■ ü 
L AfT i.. J 
10 20 30 40 50 
incidence angle [°] 
Figure 8. Intensity values vs. incidence angle coloured by the 
flight number: a) original data, b) normalized data. 
From all other flights we observe always two cluster caused by 
the roof of the main building and an extension of it with 
different normal vector. Both belong to the same region. To 
give an example, for flight 7 we have incidence angles for 25° 
and 50° and for flight 5 for 6° and 31°, as examples. The total 
number of points inside this region is 1055. The number of 
points belonging to the different flights can be seen in 
Table 2. The ratio of the variation coefficients for this region is 
R v = 0.68 , subsequently the normalized intensity value is 32% 
better than the original one. 
Flight 
2 
3 
4 
5 
7 
Points 
77 
156 
259 
308 
255 
Table 2. Number of points in the selected region measured by 
the corresponding flights. 
Based on the high variation of the intensity before and after 
normalization by the cosine law, we suppose, that the influence 
of surface effects like the kind of material or local geometry can 
not be ignored for man-made surfaces. In contrast to this Lutz et 
al. (2003) observe high variations for the intensity values for 
natural materials. 
5.5 Adaptation of the Lambertian Law 
The reflectance may not be always in accordance with the 
Lambertian law. Adapting the Lambertian cosine law and trying 
to minimize the variation coefficient for each region separately 
by varying the power p of cos(<9) p the best values are 
achieved for powers between 0.5 and 1.1 (Figure 9).