ISPRS Commission III, Vol.34, Part 3A ,,Photogrammetric Computer Vision", Graz, 2002 
  
linear features, some tie and control points in a self-calibration 
process to estimate the following parameters: 
e The EOP of the involved imagery and the IOP of the 
involved cameras. 
e The ground coordinates of tie points and the 
parameters defining the straight lines in the object 
space. 
As shown in Figure 1, for a frame camera, a straight line in the 
object space will be a straight line in the image space in the 
absence of distortions. Deviation from straightness in the image 
space is a function of the distortion parameters. As mentioned 
before, including straight lines in the bundle adjustment 
procedure would require the answer to two main questions. 
First, what is the most convenient model for representing 
straight lines in the object and image space? Second, how can 
we establish the perspective relationship between image and 
object space lines? In this research, two points along the line 
represent object space line. Those points are monoscopically 
measured in one or two images within which this line appears. 
The relationship between those points and the corresponding 
object space points is modelled by the collinearity equations 
(Equations 4 and 5). In the image space, the lines will be 
defined by a sequence of intermediate points along the line. 
Once again, those points are monoscopically measured (there is 
no need to identify conjugate points in overlapping images). 
This representation is useful since it allows us to individually 
model and include the distortions at each of these points. The 
perspective relationship between image and object space lines is 
incorporated in a mathematical constraint. The underlying 
principle in this constraint is that the vector from the 
perspective centre to any intermediate image point along the 
line lies on the plane defined by the perspective centre of that 
image and the two points defining the straight line in the object 
space. In other words, the three vectors (Figures 1 and 2): 
eV, (the vector connecting the perspective centre to the 
first point along the object space line). 
e V, (the vector connecting the perspective centre to the 
second point along the object space line). 
e V, (the vector connecting the perspective centre to 
any intermediate point along the image line) are 
coplanar (Equation 6). 
(9 xV,). P, =0 (6) 
  
Figure 1. 3-D straight lines in frame camera imagery. 
A - 146 
(Xp 0: ZO D ,K ) 
  
  
  
   
  
p 
uL 
1=1 X -Yo 7 y X 
Z p (x, 
(X, Y Zi) (X5, Yo Z,) 
x-x, — distortion, 
V, = R(® ,0 ,K ) y—y, - distortion, 
-—C 
Figure 2. Mathematical model for including straight lines in 
frame camera imagery. 
Equation 6 incorporates the image coordinates of the 
intermediate point, EOP, IOP (which includes the distortion 
parameters) as well as the ground coordinates of the points 
defining the object space line. The constraint in Equation 6 can 
be written for each intermediate point along the line in the 
imagery. One should note that this constraint would not 
introduce any new parameters. The number of constraints is 
equal to the number of measured intermediate points along the 
image line. 
  
  
a A x 
= ^x 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
Image 1 Image 2 
wc à 
a Xe a 
^N ^w y 
Ne 
Image 3 Image 4 
(A) 
1 
a \ a 
| x 
A Fg Va 
7M 
Image 1 Image 2 
d Ky, ? 
2 
Image 3 Image 4 
(B) 
e Points defining the line in the object space 
X Intermediate Points 
Figure 3. Schematic drawing representing two scenarios for the 
selection of the end and intermediate points in 
overlapping images.