o 
- 6 = 
The preliminary results of the comparisons with real image 
data are rather promising. I am convinced the method will work 
at best even in the case of testfield 3 if the orientation 
angles for each image could be introduced. This will be now 
confirmed by regarding the condition numbers and correlation 
values of the pertaining normal equations. 
5. NUMERICAL STABILITY AND CORRELATION VALUES OF THE 
CALIBRATION METHOD 
We first compute the spectral condition numbers for the normal 
equations without having introduced the orientation angles. 
Starting from the design matrix A of table 2, see /1/, we have 
to compute cond, (AT PA) = cond„(N), for abbreviation. Since 
we used for the solution of the normals the CHOLESKY -decom= 
position, which belongs to the scaling-invariant procedures 
/2/, /3/, the minimum condition number with respect to scaling 
operations should be taken as a measure for numerical stability. 
The computation of minimum scaling is by far too complicated 
for general matrices. So we used the wellknown near-optimal 
scaling procedure which results in equal diagonal elements. 
This matrix will be denoted as N. As can be realized from the 
following table the differences between cond, (N) and cond, (N) 
are rather considerable! 
Table 1: Spectral condition number of normal equations without 
introducing the readings of orientation angles 
  
  
  
  
TESTFIELD 
1 2 3 
series of cond, (N) cond, (N) cond, (N) 
photos cond, (I) 
27 
1 1, 8:640 15 1094 05 3,7 : 10° 
4,8 - 10° 
27 
2 5,7 2,5 « 105 1,7 + 10? 
4,8 + 10 
28 
3 1,4 9 10 2,5 : 10° 1,7 i 10° 
4,8 » 107