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