Devin Kelley 
  
types are easily derived from this model, and implemented by fixing some of the parameters of the panoramic model, 
The perspective transformation model for point features in linear array scanners is as follows. 
EL ; Nx (1) 
x, = X, +imelt)—c D 
y, 7 Yp MENS 
2 D 
where 
NomnX At Ca LE Zi) 
X 
N. =pn(X,~-X +n, - Yi) + 15(Z, -Z5) 
y 
Dzr(X, —Xletruy -YX)rerLq(,-21) 
x ; y : image coordinate measurement of point a at time t 
X,.Y,.Z,: object coordinates of point A 
Xp. Yp.C: calibrated principal point position and principal distance of the camera 
T T 
y' : HE nt : time dependent elements of the combined rotation matrices R^ (&,)R' (0,,0,, K,) 
0,: scan angle for panoramic sensor at time t 
imc(t): image motion compensation at time t 
X i ; Y! „zZ 0 : time dependent object coordinates of the perspective center 
2.2. Straight-line constraint for frame imagery 
Habib (1999) introduced a straight-line constraint for the bundle adjustment with frame imagery. This function 
constrains the perspective center of any image, the image line and any object point that belongs to that line to be 
coplanar. The constraint is implemented in the following way. 
In one image, two points are measured to define the object line (see Figure 3). The image and object points are related 
by the collinearity equations. These points do not need to be visible in subsequent images. In each subsequent image, 
the image line is represented by polar coordinates (Eq. 2). 
. X:cosÓ, * y:sinO; - p, 
Which can also be written as: 
x | fe cos, 
y |-|c-sin0,1=0 © 
m Pi 
The two points defining the object line can be projected into the image space of the i" image by the collinearity 
equations (Eq. 4) and must satisfy the equation of the line (Eq. 3). 
X, XoXo 
va =A-R VY =o (4) 
"C Z Lu 
Finally, the constraint relating the i" image line with any of the points along the object line can be defined as follows. 
X,7Xyllc:cosó 5 
RI .| Y,-Y, |:|c:sinQ |20 
Z,- £y p 
  
180 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B1. Amsterdam 2000. 
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