The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
segments found on a QuickBird image of a rural area. Object 
structures consisting straight line segments can be found in roof 
structures, straight road segments and bridges as well as boarder 
lines of field. Typically urban area offers a rich variety of such 
line structures, but also in rural areas there usually exist plenty 
of line segments to be detected and sometimes fairly long as 
well. It has to be remembered that uniform orientation of object 
lines does not provide enough information to solve the 
projection differences of images. Fortunately, there are no 
difficulties to find line segments with varying orientation in 
urban areas. Instead, in rural areas the variety of straight line 
segments is naturally more modest. But field borders are often 
straight and fairly long and also country roads frequently 
consist of fairly long straight lines. In this sense, use of lines for 
image registration is not restricted only to urban areas. 
The image registration algorithm used in this research is based 
on eight parameter projective transformation between 2D 
parametric line equations. This approach has been earlier used 
by (Weerawong,1995), (Barakat et.al.,2004) also good 
presentation of used method can be found in (Mikhail 
et.all.,2001). Long line segments are preferable in order to 
determine 2D line parameters reliably since line parameters are 
the only observations in determination of the projective 
transformation. In real world case, it was found that line 
segments shorter than 30 pixels long should not be used. In 
determination of 2D line parameters and projective 
transformation LSQ estimation model was used. 
2. USED METHOD 
In aerial photography linear features and especially feature line 
segments have been used to solve exterior orientation of a 
sensor as well as intersect new object lines from two or multiple 
images. In formulation the image observations, projection 
center and object line parameters have been tied together in 
order to solve unknown sensor orientation. However, this 
requires some information about the imaging device, especially 
the focal length and lens distortion values. Unfortunately, this 
information is not available in case of satellite images. 
Therefore it is sensible to apply line based transformation in 2D. 
In this study line parameters are used as observations in order to 
solve the projective transformation between two data sets. The 
2D projective transformation is a rectification between two 
planes imaged through perspective projection. This is only 
partly true with satellite images like QuickBird imagery. In row 
wise this requirement stands, but in column wise the imaging is 
closer to orthographic projection and in case of QuickBird the 
motion compensation even more violates this requirement. 
Even though this deficiency has not been considered to be 
crucial. 
Figure 1 Presentation of parametric straight line 
First, in calculation of projective transformation based on lines 
one must construct a parametric presentation of a line. This 
must be done for both data sets. The parametric presentation of 
line binds all the points (image or geographic points) 
belonging to this particular line. 
There are at least two sets of parameters that can be used to 
represent line in 2D space. One is based on angle a and distance 
d from origin, see equation 1. 
L — x* cos« + y * sin« — d — 0 
(1) 
The same line can be expressed with coefficients a and b in 
normalized line equation, see equation 2. 
L = ax + by +1 
(2) 
We can get from equation 1 to 2 easily by applying equation 3. 
[a = -cos aid 
[¿> = -sin aid 
(3) 
It has to be noticed that both equations are ambiquous in case 
the line goes through the origin. In order to avoid such a case 
origin has to be shifted in computation of line parameters. 
The point based projective transformation has eight parameters 
and minimum number of point observation is four (4) points not 
all lying on the same line, see equation 4. Similar equation can 
be constructed between line parameters derived from two 
different data sets, see equation 5. However, the parameters 
derived from line coefficients are not the same as parameters 
derived from point observations. 
x ' _ e l x + f l y + g l 
e 0 x + f 0 y + l 
• _ e 2 x + f 2 y + g 2 
e 0 * + /o.y + 1 
(4) 
r x a + s x b + t x 
r 0 a + s 0 b +1 
r 2 a + s 2 b + t 2 
r 0 a + s 0 b +1 
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