Devin Kelley 
  
The multiplication with the rotation matrix R, transforms the vector into the ground coordinate system. 
The vector from the perspective center to the first object point along the line is defined as: 
X 1 X 0 
Yızl Ye Ye 0 
Z, = Zo 
The vector from the perspective center to the second object point along the line is defined as: 
Ix x (8 
;7| Y; - Yo 
Z,-Z 
Both vectors (Eq. 7 and 8) are defined with respect to the ground coordinate system. 
As illustrated in Figure 5, the vectors from the perspective center to each scene point along the line should lie on the 
plane that is defined by the perspective center and the two object points defining the straight line. This condition can be 
formulated as: 
(V, xV,) eV, 20 
Pct) (X5.Y5,25,0 ,9, K^) 
    
  
  
X, Y Z) (X5, Y» Zn) 
Figure 5: Plane defined by two object points and the perspective center. 
This constraint for straight lines in aerial triangulation is a function of the following parameters. 
F(X,Y,2,, X, Y,,2,, X5, Yo, Z5,0 9! x, y)z0 (10) 
The unknown parameters are the EOPs of the images and the ground coordinates of the two points (A&B) defining the 
line. These two points are measured in one scene. In each scene that the line is visible, the constraint (Eq. 9) can be 
applied to all points measured along the line, regardless of whether or not the defining points are visible. Because the 
EOPs change from one point to the next, the number of independent constraints will equal the number of measured 
points along the line. The ground coordinates of the supplemental points along the straight line are not determined 
during the bundle adjustment. These measured points only contribute to increase the geometric strength of the 
adjustment. 
The constraint can also be applied to frame imagery. In this case, only two independent constraints can be generated 
per image, due to the fact that there is only one set of EOPs associated with a single image. 
  
182 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B1. Amsterdam 2000. 
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