Facade Reconstruction of Destroyed Buildings Using Historical Photographs 
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Another effect of the replacement procedure which should be considered is surely not desired. There may occur systematic errors of 
the position of the replaced objects. For example in some facade images, the windows in some area of the image may be slightly 
shifted. This systematic error occurs when the window planes are a little bit behind the main facade plane and should be reduced by 
a-priori knowledge. For instance it could be assumed that the horizontal distance between neighboured windows in the same floor 
are always equal. Then the detected distance of the other part of the image or an average value could be used. Finally, advantages 
and disadvantages of an actual replacement procedure should be evaluated by the fact, whether an improvement of the desired result 
is reached. The procedure of object replacement, of course, always needs some certain effort of interaction with the user. Similar to 
the object replacement procedure using repetitions is the symmetric completion. The SDR technique may be used again to find 
automatically the symmetry axis. In our example (see Fig. 11) this was used to produce the view of the stairs. 
5. RESULTS 
A number of images was analysed with the presented methods. The quality of the resulting rectified facade views was different and 
can often evaluated only intuitively (see Fig. 12). In the case of destroyed buildings it is very difficult to estimate the error of meas 
urements obtained by the rectified images if no camera information is available. Therefore several reproducibility experiments have 
been performed with existing objects and cameras. In the following the experiments are described and the main quantitative results 
are given. A more detailed documentation of the results has already been published (Brauer-Burchardt and Voss 2001). 
In the first experiment we tried to estimate the accuracy of the principal point determination using three vanishing points. We imaged 
a number of buildings with a SLR-camera and calculated the principal point co-ordinates according to the model described in section 
2.2. The coefficients of variation for the principal point co-ordinates were about 5% and for the focal length 1.4%. The error of the 
metric measurement resulting from the erroneous intrinsic camera parameters depends on the error of vanishing point calculation and 
additionally on the angle between the optical axis of the camera and the normal vectors of the rectified planes. Thus this error is 
difficult to estimate. We reconstructed a building with known measures and determined the mean percentage error of the aspect ratio 
of all its facades. The coefficient of variation was found to be about 2%. Additionally, the error of the principal point co-ordinates 
using the method described in section 3.2 was determined by the following experiment. A number of photographs of buildings with 
the requested property of an equal aspect ratio on different facades was made by a horizontal adjusted camera without changing the 
camera parameters. We used pairs of points with short, medium, and long distances for the aspect ratio and considered different 
angles (15°/75° up to 45°/45°) between optical axis and facade normal vectors. Whereas longer distances between the points of the 
same length ratio improved the accuracy, no significant angle dependence could be found. 
Figure 12 shows a possible negative effect in image rectification. Whereas the facade of the right building seems to be correctly 
rectified, the facade of the left house is not. This results from the deviation of the supported preconditions. In this case the facades 
are not in parallel planes which requires the separate analysis and more interactive effort. 
Fig. 12: Rectified view of the image shown in Fig. 2. 
6. SUMMARY, DISCUSSION, AND OUTLOOK 
A methodology to produce similarity mappings of planar surfaces with the input material of only single view photographs was pre 
sented. The technique is deemed suitable to reconstruct destroyed historical buildings or parts of them since there is a lack of consid 
erable information such as architectural records and camera information. We depicted the use of feature conditions such as linearity, 
parallelism, perpendicularity, and symmetry together with vanishing points for the metric reconstruction of plane facades of the 
imaged buildings. 
Concerning the geometric constraints our methodology is similar to others (van den Heuvel 1998, Becker 1995), especially in rela 
tion to vanishing points and perpendicularity. But we did neither focus here on probabilistic representations for uncertain geometry 
nor the determination of absolute orientation. A comparative study with the methods of other authors concerning the uncertainty of 
reconstructed measures has not yet been performed but should be one of the aspects of our future work.