Reconstruction from a Single Architectural Image from the Meydenbauer Archives 
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3.2 Vanishing point detection 
When straight image lines have been extracted the parameters of interior orientation are determined by applying two types of object 
constraints. First, parallelism assumptions of object edges are applied. Second, perpendicularity is assumed for the three major object 
orientations defined by three groups of parallel edges. When lens distortion is absent, the projections of object edges that are parallel 
intersect in a point in the image called the vanishing point (Figure 4). With the detection of a vanishing point the parallelism of the 
related object edges is assumed. 
The method for vanishing point detection was designed to make use of the assumption of perpendicularity between the three main 
object orientations (van den Heuvel, 1998a). However, when principal point and effective focal length are unknown only parallelism 
assumptions can be used in the vanishing point detection procedure. Projections of parallel object edges intersect in a vanishing point 
independent of the location of the principal point or the focal length. The perpendicularity assumption is introduced to allow the 
estimation of the interior orientation parameters (section 0). 
Figure 4: Vanishing point as the intersection of the projections of parallel lines in object space 
The method for vanishing point detection is based on the statistical testing of the intersection hypotheses of combinations of three 
image lines, or rather the intersection of the three interpretation planes associated with these lines. Therefore, each intersection test 
involves three normal vectors defined by two image points each. 
The procedure for the detection of the vanishing points is summarised as follows: 
The longest of all available image lines is chosen as the first line of the vanishing point. 
The test values of all combinations of this longest line and two other image lines are computed. 
Lines are clustered using the results of the testing. This usually results in several clusters. 
For the largest clusters an adjustment is set up, based on all (independent) constraints in the cluster and a line error hypothesis is 
tested for each line. 
Rejected lines are removed from the clusters and the adjustment is repeated until all remaining lines are accepted. 
The cluster with the largest number of lines is selected as the first vanishing point cluster. 
The procedure is repeated with the remaining (non-clustered) lines to detect the other two vanishing points. More details on this 
procedure are found in (van den Heuvel, 1998a).