The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part B4. Beijing 2008 
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For applications, where the intensity is of interest, a 
normalization based on the incidence angle is needed. The 
variation of the incidence angle increases if data from several 
flights with different paths are fused.To give an example a 
RGB-image together with the corresponding intensity values 
from two different flights is visualized in 
Figure 1. The viewing direction of the sensor system is depicted 
by a black arrow. The area of interest is the gabled roof. The 
roof area orientated towards the sensor systems delivers higher 
intensity values, while the turn away roof area delivers 
significant smaller intensity values. 
Figure 1: Dependency of the intensity from the incidence angle: 
a) RGB image, 
b) Intensity values of flight 3, 
c) Intensity values of flight 4. 
These from the waveform estimated values are strongly 
correlated to the incidence angle of the laser beam on the 
surface. Therefore we propose to normalize the value of the 
intensity by considering the incidence angle derived by the 
sensor and object position as well as its surface orientation. 
In Section 2 a brief description of the used full-waveform data 
is given. Further we introduce the physical constraints, the 
required normalization step, and the methodology for 
calculation of the normal vectors of the surfaces based on the 
covariance matrix and the resulting incidence angle. The 
description of the scene and the gathered data is presented in 
Section 3. In Section 4 homogenous test regions are selected for 
the assessment of the normalization. The results including a 
presentation of the values before and after the normalization are 
demonstrated in Section 5. Finally the used formula and derived 
results are discussed. 
2. METHOLOGY 
2.1 Terminology of Full-Waveform Data 
By the full-waveform laser data acquisition for each beam the 
total number of detected backscattered pulses is known and is 
assigned to the corresponding echoes. Each echo is described 
by a point with its 3d coordinate, signal amplitude a , and 
signal width w at full-width-at-half-maximum derived from the 
Gaussian approximation. Additionally the 3d coordinate of the 
sensor position is available. 
The shape of the received waveform depends on the illuminated 
surface area, especially on the material, reflectance of the 
surface and the inclination angle between the surface normal 
and the laser beam direction. The typical surface attributes 
which can be extracted from a waveform are range, elevation 
variation, and reflectance corresponding to the waveform 
features: time, width and amplitude. 
The intensity (energy) is estimated by the width multiplied with 
the amplitude of the Gaussian approximation and modified by 
the range between sensor and object with respect to the 
extinction by the air. It describes the reflectance influenced by 
geometry and material of the object at this point. For each 
particular echo caused by partially illuminated object surfaces 
we receive an own intensity value. 
2.2 Physical Constraints 
For data acquisition a monostatic laser scanning system is used. 
The received energy E r = c-a-w is calculated from amplitude 
and width of the received signal approximation. The factor c is 
constant and has therefore no influence for our consideration. 
Considering an energy balance it depends on the transmitted 
energy E t , the distance R to the object surface, and the 
incidence angle 3, which is given by the angle between the 
transmitter direction and the surface normal vector 
where C and C r are constant terms of the transmitter and the 
receiver (Kamermann, 1993; Pfeifer et al., 2007). The 
atmospheric attenuation along the way from the transmitter to 
the object and return to the receiver is describes by 
T 2 (R) = e~ 2aR . Let /(cy) entail all other influences like 
surface material and local surface geometry. This formula is 
valid for objects with larger size than the footprint of the laser 
beam. All constant terms may be ignored because at this point 
we are interested only on the behaviour of the received intensity. 
Knowing the received amplitude and width of the signal a range 
corrected intensity is calculated to 
I R =C X ■ a ■ w ■ T~ 2 (r) ■ R 2 , (2) 
where Q may be any arbitrary constant. This intensity I R 
does not dependent on the distance R anymore. For 
homogenous regions, cf. the following sections, this formula 
delivers value differences less than 5% in comparison with 
using a mean distance. This is only valid for data captured at a 
single flight path. I R is influenced by the material properties 
and the incidence angle.For all points with high planarity we 
normalized the measured intensity additionally by 
7 = /^/cos(i9) considering the incidence angle. The 
illumination direction e t is calculated from the sensor to the 
object position. The normal vector of an object surface is 
determined by the evaluation of the covariance matrix, cf. 
Section 2.3, with respect to the smallest eigenvalue T 3 and its 
eigenvector e 3 . With this normalized vectors we calculate the 
required divisor by cos(.9) = \e t °e 3 | . These correction steps 
remove known influences from the measured intensity. 
Therefore the normalized intensity / depends for the used 
wavelength on the material properties only. The influence of 
speckle effects is neglected.