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Similarly, the second order Gauss-Markov process can be defined as a gaussian random process whose conditional 
probability distribution is dependent only on the two previous points. The related fictitious observation equation is 
  
Fa =(a,), Ap, +(a,), AP; -Ap, 20 (5) 
d (1+s)-e” dAr2:) 67! d 
i-i sje 
eS p 
MEN NC (7) 
e I 
where Ap is correction of each 6 EO element 
i is line number in the image(i = 3.4....,1280) 
s is coefficient for each EO element 
Note that GM process is applied to the corrections of the six EO elements instead of the six elements themselves. 
By adding these fictitious observation equations to the conventional observation equations, 6 EO parameters for each 
image line are tied, or constrained, stochastically to other image lines in close proximity. This model allows for greater 
flexibility for linear feature constraints to contribute to parameter recovery, thereby improving rectification accuracy. 
2.3 Exploitation of Ground Line Features 
The most common control feature used in the triangulation of multispectral imagery as well as traditional frame 
photography is the control point. In our data set, the control points coordinates were obtained from triangulated frame 
photography that included the HYDICE coverage. 
Linear features can be defined as the linked edges that determine object boundaries. Although linear features have not 
been widely used in the estimation of exterior orientation (EO) for the time-dependent sensor, many experiments have 
been performed and have proven the usefulness of linear features in frame photography applications. 
For the pushbroom airborne imaging system, linear features can serve as high-density control data so that high 
frequency distortion can be detected and corrected. As can be seen from the raw HYDICE images, the linear features 
which suffer worst from roll-induced displacements occur mainly in the direction of the flight line, while linear features, 
which are almost perpendicular to the flight line, showed little distortion. Therefore, the linear features in the direction 
of across track'are not helpful to detect high frequency roll-induced distortion. 
Although the term linear feature encompasses any continuous feature with a negligible width and includes such 
parameterizations as splines, we concern ourselves with the special case of straight-line segments in the remainder of 
the paper. 
2.3.1 Control Line Model. Line can be used 
7 as control data like control point. At a given 
(Xp, Yo Zp) scan line, a image vector L3, which is rotated 
: to the ground coordinate system, is on a plane 
n? L. that is defined by the three points, two end 
plight E f T y points of the line on the ground space and the 
Qt : f Qo Y) position of instantaneous perspective center. 
VIA Therefore the determinant of the three vector in 
figure 2 should be equal to zero. The control 
fer E line model can be expressed as follows: 
  
Lz : | F,-|1 I2 13-0 (8). 
: To Ground Point 
. where 
Az X, - x, V-h Z-zr 
(X», Y», Z7) I2zix, X, y =} Zu al. 
C, Y Z) ia 
  
  
  
L3=M'|x y -fÏ 
Figure 2 Control Line Model 
2.3.2 Constrained Line Model. Straight-line 
features also can be used to constrain point observations on a line. Note that image vectors on a given line are nearly 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B7. Amsterdam 2000. 185