unction 
e to be 
related 
image i, 
(2) 
3) 
inearity 
(4) 
lows. 
(5) 
Devin Kelley 
  
Here, À is ignored because Xz0. 
In summary, there are two steps to implementing this constraint. First, in one image, the straight line is defined by 
measuring two points (A&B), generating four collinearity equations (Figure 3). Next, in each subsequent overlapping 
image, that line is defined in terms of polar coordinates- adding two independent constraint equations for A and B. It is 
important to note that in each overlapping image, no more than two independent constraint equations can be generated 
for a particular line. 
  
Figure 3: Geometry of the straight-line constraint for frame imagery. 
3. STRAIGHT LINES IN LINEAR ARRAY SCANNER IMAGERY 
The underlying principal in the straight-line constraint for linear array scanner imagery is that the vector from the 
perspective center to a scene point on a straight-line feature lies on the plane defined by the perspective center and the 
two object points defining the straight line. In object space, straight lines are to be represented by two points along the 
line. The corresponding line in image space will be represented as a sequence of points that may not lie on a straight 
line. 
  
Figure 4: Perspective geometry and straight lines in linear array scanner imagery. 
As shown in Figure 4, two points in one scene are used to define a straight line in object space. The object point, the 
corresponding image point and the perspective center of the exposure station lie on a single light ray. Therefore, the 
generalized collinearity equations (Eq. 1) can be applied to each of the two points defining the line. 
For each image, the vector from the perspective center to any image point along the line can be defined with respect to 
the ground coordinate system as: 
xX—X, 
V, 2 R(o' ,o', x!) y", (6) 
~C 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B1. Amsterdam 2000. 181