Manfred Weisensee 
  
When choosing a grid spacing in object space equivalent to image resolution, the entire information content of the 
images is used. 
In equation (12) three groups of unknown parameters can be distinguished and treated separately in an iterative 
parameter estimation, cf. /Weisensee 1992/: 
the changes dG;; of the grid values GY; of the ortho image G(X, Y), 
the parameters of the transfer functions T', T", ... and 
the changes dZ;; of the grid values Z; of the surface Z(X,Y). 
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Given the interior and exterior orientation of the images G', G", ... and some approximations of Z;;, the parameters G; = 
G%; + dG;; can be computed directly by the mean values of G'(X, Y), G'(X,Y), ... resulting from the image functions 
G'(x',y), G"(x",y"), .... The parameters of the transfer functions T', T", ... are then computable from the mean values and 
the variances of the histograms of G'(X,Y), G"(X,Y), ... . The remaining group of unknown parameters dZi has to be 
estimated by solving the normal equation system resulting from equation (12) which is a band matrix, that can 
effectively be processed. 
The number of iterations needed to arrive at the final result primarily depends on the quality of the approximate values 
of the surface Z(X,Y). Several strategies have been applied to decrease the demands on the approximations, e.g. using 
image pyramids and progressive refinement of the surface model, /Korten et al. 1988/. But, the availability of laser 
scanning data dramatically decreases the number of iterations, because in the ideal case of undisturbed reflection of the 
laser beam, the approximations are very close to the final solution. 
3 LASER SCANNING 
Although laser scanning systems are only available on a broad basis since less than a decade, already a large number of 
publications is at hand, which give insight in most of the concepts, technical details, algorithms and applications of this 
technique. In this paper, laser scanning data is considered as the raw coordinates P(X,Y,Z) resulting also from different 
types of additional measurements (GPS, INS). For further information the reader is referred to the literature, e.g. special 
issues of journals /Baltsavias 1999/ and /Steinborn and Fritsch 1999/ or /Fritsch and Spiller 1999/. 
The so called raw coordinates of laser scanning give those positions on an object surface, where a laser beam has been 
reflected first or last, depending on the registration mode of the system. Furthermore, some systems record the intensity 
of the reflected laser beam, which results in a digital image - usually in the near infrared channel - of the surface. Such 
images can be directly introduced in a surface reconstruction according to equation (12) when applying a suitable model 
for the image forming process. And, the information given by the images would be sufficient for the reconstruction of 
the surface, provided that an adequate overlap of flight strips is given. For most surfaces the difference between 
recording first and last reflection merely shows the roughness of the surface or the ability of the system to reproduce a 
result. Figures for the accuracy of such points are given by standard deviations between laser scanning and control areas 
from 5 cm to approximately 1 m, depending on a large number of parameters like height and speed of the platform. In 
forest areas the difference between first and last reflection gives the height of the trees - an extreme case of surface 
roughness. Depending on the type of wood, different percentages of points are reflected in the foliage or on the ground. 
Here, penetration rates between 30% and 7096 have been reported. Points that are reflected in the foliage correspond to 
the surface that is reconstructed by photogrammetric methods, although in wooded areas photogrammetry lacks similar 
deficiencies as laser scanning. 
4 COMBINED ADJUSTMENT 
Introducing laser scanning data into FastVision can easily be accomplished when using the bilinear interpolation given 
in equation (7) and the separation of the grid Zi; into approximations Z^ and their corrections dZ; given in equations 
(10) and (11). With equation (7) first approximations for the iterative parameter estimation of FastVision can be 
computed directly by utilizing the raw coordinates P(X,Y,Z) as observations in 
2 
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968 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
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