Use of Object Geometry to Locate Vanishing Points 
Direct application of equations (7) through (12) permits computation of the 
vanishing point coordinates from the elements of the interior orientation and exterior 
orientation matrix. However, the problem mostly confronted is that of computing the 
elements of the interior orientation and exterior orientation matrix from the coordinates 
of the vanishing points. This implies that some independent means must be provided for 
location of the vanishing points. This is accomplished by using the geometrical properties 
of the object imaged in the photograph. The properties which are best exploited are 
parallel lines and the segmentation of a line in known proportions. 
Parallel Lines - A family of parallel lines in the object space ís imaged in 
the photograph as a set of lines converging toward and terminating at the vanishing point. 
Hence, the vanishing point of two or more parallel lines may be located by producing the 
images of these lines to intersection. 
The intersection of two line images is found analytically by solving the 
equations of the lines for the image coordinates x and y. The equation of each line 
image is obtainable from the coordinates of two image points on the line. Figure 3 shows 
the images of two parallel lines converging toward their vanishing point, n. P11 and P19 
are two points on the image of line 1, and Psy and P5 are two points on the image of 
line 2. The coordinates of the vanishing point, n, can then be computed as: 
  
et ora) 
- - 7 / 
- ud - / 
_ - = Zz 
7 
Line 1 P125 04533415) / 
/ 
/ 
P441 04,9313? / 
f 
/ 
P235 0X5533 55) 
Line 2 
Po 5513354? 
  
  
  
Figure 3