4.3 Dimensions of Patches and Windows 
The dimensions of the windows depend on the expected X,y shifts of the patches. The shifts 
depend on the Z - derivatives of the collinearity equations and the height approximation. The Z - 
derivatives again depend on the exterior and interior orientation of the sensors and the location 
of the match points in the image system. 
A small change in Z leaves the derivatives almost unaffected, so practically the derivatives can be 
considered constant throughout the iterations. Hence the dimensions of the windows are a 
function of the unknown height error only. Assuming a limit for the maximum possible height 
error, we can determine the window dimensions. If good height approximations exist, this will 
result in small window dimensions and thus in storage and computing time savings. 
It is useful to choose the patch dimensions such that at least a part of the signal of the correct 
match points is included in the patches. A ratio of three between x,y half dimension of the 
patches and maximum absolute x,y shift proved to be generally satisfactory. Given a certain ratio, 
the dimensions depend on the shifts and can be computed from a maximum possible height 
error. 
But this procedure is not sufficient. The dimensions must also conform to the specific signal 
content. There may be cases of poor signal content, where the dimensions should be increased 
beyond the above mentioned ratio in one or both directions to include significant signal (e.g. 
edges) or cases of very good but small signals on uniform background, where the dimensions 
should be decreased. 
As a result, a combination of an a priori signal content analysis and the use of an estimated 
maximum height error is recommended. The problem of determining the patches dimensions 
however is basically solved, if the starting height approximations are good. In this case the signal 
content analysis, which can be difficult and computationally expensive, becomes much less 
important and can be omitted. 
4.4 Pull-in Range ( Convergence Radius ) 
It is known that pull-in range strongly depends on the signal structure, including both geometric 
and radiometric characteristics. It increases when low frequencies are dominant in the signal. 
They should not be very low though because then the signal would not be distinctive and it 
could be easily contaminated by noise. Good signals do not necessarily have a large pull-in 
range. Sharp, small targets on uniform background (in the extreme case an impulse Delta 
function) have a very poor pull-in range. On the contrary, if edges extend from the correct match 
point to the wrong starting position, then the pull-in range increases. Pull-in range also increases 
with higher SNR, e.g. by increasing the patch dimensions or smoothing. 
The convergence behaviour without smoothing was as follows: 
i) ForAZ 2 0.5 m (corresponding to a parallax convergence radius of 45.3 um $ 2,3 pi) and a 
dimension ratio of 3, all points converged successfully. 
ii) For AZ = 1.25 m (corresponding to a parallax convergence radius of 113.2 um = 5.7 pi) and a 
dimension ratio of 2, seven points converged well, two converged very slowly, two 
converged with final height 7-8 cm off the bundle heights and seven did not converge. 
With the exception of the first seven points, all others were rerun with other dimensions. 
When the dimensions suited the given signal, the runs were successful. 
Use of a 3 x 3 local average smoothing considerably improved the convergence radius (compare 
Table 2). 
It is clear from the above that a signal content analysis based determination of the patch 
dimensions and smoothing increases the success rate and pull-in range. It should be noted 
though that smoothing and large dimensions might slightly decrease positional precision and 
might result in slightly different parallaxes and final heights. 
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