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livided into 
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0. and 6 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B1. Istanbul 2004 
     
  
The relative azimuth of viewing and illumination directions was 
determined on the slanting plane and vectors were thus 
projected onto that plane. Point Æ = 7, and surface normal n 
uniquely define a plane in E? space; point PS r 
plane if and only if 
lies on this 
#-(F-ñ)=0. (3a) 
Written in three-dimensional coordinates, the plane equation 
becomes 
MX+My+MZ=N-h=d, (3b) 
where n; are the components of the surface normal. 
By setting 7 = 0 , the plane origin equals the origin of £^. Let 
us relocate the surface normal and viewing and illumination 
vectors to this origin. Thus d=0 in equation (3b), because # is 
now perpendicular to any vector lying on the plane. Projections 
of vectors 5 and € on xy-plane are denoted by s and c and 
are derived by setting the third coordinate of s and c to zero. 
Projections § and ¢ on an arbitrary surface can be derived by 
solving the following equation 
—MX — M9 Y 
za 2" M #0, (4) 
#3 
where x and y are first two components of vector s or c .The 
relative azimuth of viewing and illumination directions on an 
arbitrary surface is then calculated. 
2.9 Atmospheric effects 
Atmospheric influence on electromagnetic radiation is a severe 
obstacle to remote sensing. In image analysis and interpretation 
of aerial images, one typically has difficulties due to the 
different effects caused by atmospheric scattering and weather 
conditions (Widen, 1999). The atmosphere has an influence on 
the measured signal comparable to the BRDF effect on the 
ground (Beisl, 2001) and can drastically alter the spectral nature 
of the radiation at-sensor level (Schowengerdt, 1997). 
Atmospheric effects must therefore be eliminated before any 
analysis (Beisl, 2001). 
The atmospheric influence on HRSC-A images was reduced by 
estimating the atmospheric parameters from the images 
themselves. The dark object subtraction (DOS) was chosen as a 
method for correcting” of the images for atmospheric effects. 
This method focuses on estimating the upwelling atmospheric 
path radiance, with the view path transmittance assumed to be 
one. This assumption is reasonable. enough, since the path 
radiance is the most dominant atmospheric effect in the visible 
spectral region (Showengerdt, 1997). The use of DOS, as 
documented, does not hinder application of more developed 
methods such as ATCOR (Richter, 2000) for later atmospheric 
correction of sampled data. 
DOS coefficients were determined for each image strip by 
histogram analysis. The DOS coefficient of an image was first 
set at zero and then incremented stepwise by one. Pixels 
representing the current value were inspected, and if they were 
acceptable as a dark object, the coefficient was incremented and 
the evaluation performed again. 
  
Figure 2. The effect of DOS. 
2.10 Classification 
A target represented by a single sample point was identified by 
classifying the images with a maximum likelihood classifier and 
by manual clustering. DOS-corrected images were fused by 
constructing four image mosaics for a flight period, one per 
flying direction. Consequently the sun movements could be 
taken into account more precisely in the sampling process. 
The primary classification was conducted manually, using 
visual interpretation of the HRSC-A images, maps, terrestrial 
photographs and field investigations performed at the time of 
image acquisition. Although some of the classes are not fully 
identified for species, they are thoroughly clustered. For the 
Kuckuberg test site, primary classification was performed in a 
manner similar to that of the Sjókulla area, but border areas 
between different class types were left out. 
A maximum likelihood classifier was used to construct the 
secondary classification. Three parallel HRSC-A images and a 
conducted normalised difference vegetation index (NDVI) were 
used as input. The initials for image clustering were calculated 
from statistics on the images using principal axis means. 
Classification was performed with a 98% convergence 
threshold. 
The secondary classification can be used in data analysis, for 
instance to distinguish deep shadowed targets from the others. It 
also provides additional information on internal variation within 
a target class caused by soil moisture, vegetation closure 
(sparseness) and other such factors. 
3. RESULTS AND DISCUSSION 
3.1 Sampling 
The image sampling is illustrated in Figure 3. Iteratively solved 
samples are shown on top of a sampled image strip (50 points 
per line). The residual for viewing direction was 0.2?. This is 
considered to be reasonable and acceptable for the 
determination of bidirectional reflectance. The developed 
algorithms were found to be efficient and operational for this 
purpose.