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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