For the first test we simulate the imaging process. The DTM, 
the orientation of two images and an orthophoto are given 
and the two images are generated by resampling from the 
orthophoto. For each of the image pixels the corresponding 
point location in the orthophoto is found iteratively by a nu- 
merical difference scheme. Consequently the only differences 
between this two images are of geometric nature. Now an 
error is introduced into the DTM and the stereo orthophotos 
are derived using the imagery found by the simulated imag- 
ing process. The differences between the stereo orthophotos 
are directly (uniquely) the consequence of the error in the 
DTM. The results applying the linear regression model (A), 
the FE-procedure (B) and the DOP-procedure (C) are shown 
in figures 2, 3 and 4, respectively. 
That the error is very well indicated by procedure A (figure 
2) could be expected, because the idealized assumptions of 
the simulated imaging process fit well to the simple model. 
Because of this the form of the introduced DTM error which 
approximates a cross can be seen quite nice in figure 2. In 
exactly five neighboring points of the DTM an error of 3 
m in elevation is added. More surprising is that with the 
FE-procedure just in this case difficulties arise. The residual 
images €, and € show noise as expected. In the difference 
surface (figure 3), for which in the case of this figure a grid 
spacing of 5 times the orthophoto pixel size is chosen, the 
error can be recognized but much less distinct than expected. 
Coarsening the resolution of this difference surface amplifies 
the visual impression of the error but up to a spacing distance 
of 10 times the pixel size. For larger spacing distances the 
response in the difference image is lost. Neglecting the fine 
grained lowest level of the DOP, the next three bandpass 
levels of the DOP (figure 4) all indicate the error. So with 
procedure A and C the approximate position of the error is 
simply located and roughly size and form of the erroneous 
region could be found. 
The second test then uses the two images without modifica- 
tion, i. e. just as they have been digitized from the aerial 
photos (figure 1). From these two images the correspond- 
ing orthophotos are derived by differential resampling. The 
same DTM with the identical error as in the first test with 
the simulated idealized imaging process was used. The stereo 
orthophotos are plotted in figure 5. If viewing this image pair 
stereoscopically the DTM error as well some trees which are 
not represented in the DTM can be observed. The results 
applying the linear regression model, the FE-procedure and 
the DOP-procedure again are shown in figures 6, 7/8 and 9, 
respectively. 
The residual image which results from linear regression gives 
some indications about the D'TM errors as can be seen from 
figure 6. Plotted in this figure is the thresholded residual 
image, i. e. only those residuals which are larger than two 
times the standard deviation. The black blobs in the lower 
left and right of this image correspond to trees. Figure 7 
gives an impression of a residual image estimated by the 
FE-approach. Typical for this FE-residuals is that, as can be 
seen in figure 7, only noise is present. The difference surface 
(figure 8) shows large systematic differences between the two 
orthophotos. Hardly to recognize are some indications to 
trees, and practically nothing is to see from the D'TM error 
in this data. The last images (figure 9) show the first four 
bandpass levels of the DOP. On the coarse levels 2 and 3 the 
trees can be recognized. The DTM error shows up slightly 
on level 2. 
236 
in total, this real example reveals considerable problems 
which arise when the radiometric distortions between the im- 
ages are large. If the radiometric transformation is very flex- 
ible as in the case of the FE-model, the resulting error terms 
indicate that the transformation works satisfactory. Unfor- 
tunately the situation for localizing DTM errors in this case 
is just inverse, i. e. the errors are also taken away with the 
transformation. More promising are the more simple proce- 
dures based on regression as well as on image pyramids. 
4 CONCLUSION 
In this paper we followed a pragmatic line of investigation: 
at first we have explored some experiments to gain insight 
into problems we meet on the way to automatic DTM ver- 
ification. To eliminate differences between stereo orthopho- 
tos arising from distinct physical processes we used a simple 
model based on linear regression and a more complex pro- 
cedure based on modelling differences by a finite element 
surface. The idea behind the third procedure is multiscale 
(bandpass) analysis, used to separate events arising at dif- 
ferent scales. 
The example chosen for this experiments are real images with 
considerable radiometric differences. In summary, with this 
image data, all three procedures have problems in detect- 
ing inconsistencies, which result from differences between 
real world geometry and the DTM. The more complex FE- 
approach seems to eliminate too much, so that nearly no 
hints to the DTM errors remain. The more simple and 
computational more efficient approaches based on regres- 
sion analysis as well as on bandpass DOPs seem to be 
more promising. This especially holds true for imagery in 
which systematic differences between the image intensities 
are small. The results found based on the simulated imaging 
process support this observation. 
One direction of future work is to explore the information in- 
herent in the symbolic level of image representation. Though 
our first experiments with edge images have not been very 
encouraging, we expect that the less sensitivity to physical 
effects will lead to an improvement for the verification task. 
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Ackermann, F., Krzystek, P. (1991): MATCH-T: Auto- 
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Blachut, T.J. (1971):  Stereo-Orthophoto Systems. 
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