The other solution uses a technique related to the Gauss-Seidel relaxation 
method. A submatrix chosen for geometrical reasons, moves in steps across the 
original matrix. Once more the escalator matrix of Fig. 16 is seen in Fig. 18 
as the shaded area within the heavy contour lines. In a strip flown with 2/3 
overlap, five consecutive camera stations are connected by the resulting overlap 
of the photographs. Therefore, having six unknowns per station, a 30 x 30 
submatrix was chosen, which always contains such a group of unknown orientation 
  
parameters, as they belong to five consecutive camera stations. This partial 
System is now displaced along the strip by one station each time, Thus, for a 
strip with n photographs one obtains (n-4) such submatrices and consequently 
by inversion of these submatrices one obtains five values for each of the 
orientation parameters with the exception of the first and last four photographs, 
where accordingly fewer values are obtained. The arithmetic means of the roots 
of the individual parameters are now computed and considered as the result of 
any one iteration cycle. The approximation results thus obtained are used to 
  
continue the computation according to the Gauss-Seidel relaxation method, by 
changing the original absolute column, taking into account the coefficients not 
in incorporated in the individual 30 x 50 submatrices, together with the values of 
il the corresponding orientation parameters, as obtained in the preceding iteration 
cycle. The iteration is continued until the roots have converged to a pre- 
| established accuracy level. For the economy of the solution, it is of importance 
bi . that only in the first iteration cycle the individual submatrices must be in- 
ll verted. The roots in the following cycles are then determined by multiplying 
  
the individual inverses by the changed absolute columns. 
IX. SUMMARY AND CONCLUSIONS 
The analytical solution for the general problem of photogrammetry, as 
presented in this report, is not restricted by geometrical or statistical 
considerations, because all nine geometrical parameters which characterize a 
central perspective can be introduced for any number of photographs. (Compare 
[16]). Furthermore, provisions have been made to consider all types of measure- 
ments, as they may arise, as erroneous. A least squares treatment results in 
the most probable values of the unknowns of the solution, provided that the 
  
residual errors are normally distributed and the various bundles of rays are 
generated according to the principle of the central perspective. 
| 76 
  
  
zum "Aum 
RETE