to be replaced by a variable containing G,, where i 
indicates the number of the channel i of the multi- 
channel image, i.e. i runs from 1 to 3 for colour images. 
The number of equations in each Z-facet this way 
multiplies with the number of channels of the picures. 
The linear function T modelling radiometric differences 
between the images also has to be replaced by a set of 
functions, one function for each channel. The scalars £o 
and g,' become vectors gy and gy. Thus, not only the 
amount of input data and the number of observation 
equations increase threefold, but the amount of output 
data also more than doubles. The size of the system of 
normal equations grows with the number of additional 
unknowns, i.e. with the additional colour value facets. 
The other features of FAST Vision - adaptive 
regularisation to overcome the ill-posedness of the 
problem of image inversion (Wrobel et al. 1992a, Wrobel 
et al. 1992b), adaptive determination of facet size, the use 
of images pyramids (Kaiser et al, 1992) etc. - also 
remain unaltered. Again, processing starts with 
calculating approximate values for object colour values 
by using the approximate surface and one of the input 
pictures. 
In contrast to object reconstruction from grey value 
pictures colour images should be pre-processed: In order 
to minimize the correlation between the - usually three - 
colour values of each pixel a transformation of the colour 
values of the picture takes place before the application of 
FAST Vision, see next chapter. 
4. An example of surface reconstruction from colour 
images 
In order to check the computer program derived from the 
modifications of FAST Vision described above, the 
surface reconstruction was tested with the input of 
computer-generated imagery. These experiments, which 
are not shown here, proved the reliability of the new 
method by a comparison of the exactly known surface 
with the reconstructed. A next step was the application of 
the modified method to realistic image material which, in 
this case, consisted of a pair of colour aerial pictures. 
They were taken from a rural landscape in the 
southwestern part of Germany. The area is partly covered 
by buildings and vegetation. The scale of the pictures is 
1:6000, the overlap is 6096. The pictures were digitized 
with three colour channels. Fig 1-6 show the three 
channels of the left and the right image. The differences 
of the information contained in the three channels are 
obvious. Especially the lack of information about 
vegetation in the blue channel is significant. 
  
Fig.1: Blue channel of the left image. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
     
  
  
  
  
  
  
  
  
  
  
  
  
      
    
  
  
   
  
  
  
  
  
  
  
   
   
  
  
  
  
  
  
  
  
  
  
  
  
    
   
   
   
   
   
   
  
Fig.2: Green channel of the left image. 
  
Fig.3: Red channel of the left image. 
  
Fig.4: Blue channel of the right image. 
  
Fig.5: Green channel of the right image. 
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