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object reconstruction from his photographs together with the stored camera parameters (Meydenbauer 1912). Unfortunately, many 
documents and cameras of the Meydenbauer archive have been destroyed during world war two. So one of the reasons to develop 
algorithms for facade reconstruction was to get metric properties from the Meydenbauer images without camera information. More 
information about Meydenbauer can be found (Li 1997 and Hemmleb 2001). 
Surely, in recent times methods for object reconstruction using single views have been developed and improved and numerous publi 
cations dealt with this problem. Liebowitz (1998 and 1999) proposed in his studies methods for the metric rectification of planes. His 
work involved the removal of projective and affine distortions. Van den Heuvel (1998a) gives a reconstruction method using and 
formulating geometric constraints. Becker and Bove (1995) suggested a method for 3D model extraction from uncalibrated views. 
Debevec (1996) presents a photogrammetric modeling technique. Suggestions concerning the metric rectification of a plane used by 
Hemmleb (1999) are similar to those of Liebowitz. He demonstrated this method on images of destroyed buildings. The methodol 
ogy of Petsa (1993) and Karras (1999) was based on the estimation of intrinsic camera parameters and exterior orientation by analys 
ing vanishing point co-ordinates and was also applied on images of destroyed buildings. 
Although some methods have been proposed, a number of problems still persists depending on the individual mapping conditions. 
Especially the precise determination of principal point may be a difficulty which is essential for accurate image transformations. The 
main aim of this work is to improve and complete existing reconstruction methods and to add some new procedures. 
2. IMAGE PREPOCESSING 
2.1 Radial Lens Distortion Correction 
Photographs of architectural objects are often taken using a wide-angle lens which usually suffer from radial lens distortion. Since 
the lens information is not at our disposal we have to determine if any radial distortion exists and then work for their removal. A 
methodology was developed to detect and correct these distortions using only single images. Assumptions on linearity of the imaged 
objects are explained elsewhere (Brauer-Burchardt and Voss 2000a). The distortion function can be expressed as 
1 + d 2 r'~ +d 4 r' 4 ( ^ 
with r the undistorted and r’ (measured in the image) the distorted distance of an image point to the symmetry centre P of distortion 
and coefficients d 2 and d 4 . Using this model an approach for sufficient exact calculation of the distortion coefficients d 2 and d 4 and 
the symmetry point co-ordinates of distortion under the assumption of well distributed extractable points throughout the image area 
was developed. When points on straight lines are not well distributed, the algorithm may fail. 
Since the mentioned algorithm requires only linearity, vanishing points are not required at this stage. With this we are able to deter 
mine whether significant radial lens distortion exists. The iterative algorithm works as follows: 
Input: single image with points on (3D-scene) straight lines extractable 
Output: coefficients of the distortion function and co-ordinates of the symmetry point of the radial distortion 
1. Extract points assigned to a number of n straight lines 
2. Choose a starting value for the symmetry point (usually the image centre) 
3. Calculate the distortion coefficients d 2 and d 4 within a least squares task 
4. Improve the symmetry point co-ordinates using a quality measure 
5. Test the finishing criterion, goto 3 or 6 
6. End of the algorithm 
Alternatively, depending on applicability, other methods (Becker and Bove 1995, Prescott and McLean 1997, van den Heuvel 1999) 
may be used. 
2.2 Vanishing Points and Intrinsic Camera Parameters 
In the pinhole-camera model, a bundle G of parallel straight lines intersects in one point of the image plane, the vanishing point Q of 
G. Several methods for the determination of vanishing points have been proposed, e.g. (van den Heuvel 1998b). The procedure we 
used is described elsewhere (Brauer-Burchardt and Voss 2000b) and shall not be repeated here in detail. 
Considering three orthogonal directions of the 3D-object and their vanishing points Q¡, Q 2 , and Q 2 in the image plane, it can be 
shown (Caprile and Torre 1990) that the triangle Q\Q 2 Q 2 together with the principal point P form an orthocentric system. The prin 
cipal point is the intersection point of the heights of the triangle Q\Q 2 Q 2 . Let P=(X,Y) be the principal point,/be the effective focal 
length, i.e. the distance of the projection centre from the image plane and the vanishing point co-ordinates be Q\={^\,T]\), Qz = (%2> 7 12) 
and 03=(^3, ri 3 ). Then the three vectors