From the plots it can be seen that with a large weight the alterations of the five parameters follow a
certain proportionality (see Section 4.8), whereas with a small weight, the parallax is cleared
practically in three iterations with equal but opposite shifts of the two patches. After the fourth
iteration the patches move almost identically and the alterations remain almost constant, i.e. the
correlated patches move around slowly and freely.
The importance of keeping the patches along the "relief" lines with appropriate weights
increases, as the height approximation deteriorates. A small weight, i.e. a weakly constrained
patch transformation, will lead to completely wrong results in case of a large height approximation
error, whereas with a small error, it might be tolerated. When the dimensions of the patches
increase, the weight of the constraints should be also increased.
4.2 Use of Shaping Parameters
For the data used in these investigations, the use of the four shaping parameters proved to be a
disadvantage. The scale and sheering deformations were negligible. Runs with all 18 points,
introduced height error AZ = 0.55 m, 5, = 0.001 pi, local average smoothing, convergence
criterion AZ « 2cm and all or no shaping parameters gave on the average the comparative results
listed in Table 1.
NO ALL
SHAPING SHAPING LOSS
AZ=0.5m PARAMETERS| PARAMETERS | DIFFERENCE | FACTOR
(1) (2). . (2) - (1) (IN % )
Number of iterations per point 3.9 4.4 + 0.6 + 13
CPU time per point (sec) 7.6 12.6 +5.0 + 66
Difference to bundle heights (cm) 22 2.8 +0.6 +27
Difference to bundle heights (75. hg) 0.027 0.034 + 0.007 ]
Equivalent x - parallax clearance (um) 2.0 25 + 0.5 a
Max difference to bundle heights (cm) 5.2 74 + 2.2 + 42
Max difference to bundle heights (759 hg) 0.064 0.091 + 0.027 "
Equivalent x - parallax clearance (um) 4.7 6.7 +2.0 i
Correlation coefficient 0.91 - 1. 0.92 - 1. — —
x - parallax clearance Ax is given by Ax = ( b/ hg ) AZ, with b = image base
Table 1. Shaping versus no shaping parameters
The results of the two versions are fairly close to each other with the exception of the CPU time.
Use of the shaping parameters results in higher processing times, especially for forming the
normal matrix and secondly for transforming and interpolating the right patch. It also leads to
slightly worse convergence rate and final heights.
If a good approximate height is assured, then the patch dimensions can be kept small, and if the
expected deformations in case of aerial imagery would be small, the shaping parameters may be
excluded. This issue, however, needs more research.
As a result, in the remaining investigations described below, the shaping parameters were not
used.
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