mate values for the additional parameters are available. The idea then is to keep the normal
equation matrix constant and only vary the right sides A. This would also lead to an increase of
speed and would quite well fit into a robust algorithm with modified residuals (cf. also Meyers
and Frank 1980).
The condition 8015745 Az can be used in the form u <3/¢ =,» thus yielding an upper bound for
the boundary frequency of a low pass filter which guarantees convergence if the approximate
value is supposed to be inaccurate up to zo.
The discussion of the different quality measures up to now was more or less based on the same
mathematical model for the correlation algorithm and the image. The equivalence of the matched
filter and the least squares approach could be used to advantage. The following results are based
on computer simulations alone, as especially the determination of the reliability would require
the derivation of the joint probability density function of the estimated cross covariance
function involving the fourth moments of the original signal. The results however prove to be
essential for assessing the quality of digital correlation procedures.
3.6 The reliability of digital point transfer
As already pointed out in sect. 2 the matched filter may lead to quite wrong results. This is
due to the small pull-in-range but even more to the existence of relative maxima of the crosscor-
relation function which in case of disturbancies might become the absolute maximum. The aim is to
decrease the number of false matches which can be done by trying to increase the probability of
correct matches, i.e. the reliability. The proposed filters Mos Ma and m, prove to be appropriate
for this purpose.
The results of a thorough investigation by Ehlers (1982) are shown in fig. 7a and b.He compared
5 different filters for point transfer with respect to their robustness against additional noise.
These were : a. cross correlation d
b. complex exponentiation with local variance
C. complex exponentiation with global variance
d. least sum
e. phase correlation.
Fig. 7 Reliability of point transfer using different filters. Probability of a correct match vs.
the SNR, used filters cf. text above (from Ehlers 1982) patch sizes 30x30 and 11x11
a. points with high contrast b. points with low contrast
j Reliability À Reliability
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