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The International Archives oj the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. Beijing 2008 
According to the collinearity principle, points p d and p d of 
straight line segment L 
in the straight line L r 
Mathematically, every cross products of each two vectors of a , 
b and c equal to 0 , i.e. 
ax b = 0 
axe = 0 
In details, 
(*2 - x \ )Of -y[)~(y r 2 - y r \ )Of -O = o 
(x[ - x[)(y d -y d )~ (y r 2 -y[)(x d -X d ) = 0 
Translate it to the error equations, 
Kb = ( X 2 - X 1 )Of - y[ ) - (y r 2 - y[ )0? - x[) 
Vac = ( X 2 ~ X 1 )(y d 2 -yt)~ (y r 2 ~ yi )( X 2 ~ X \ ) ( 2 } 
Taking formula (1) to equation (2), using enough number of 
corresponding straight line segments, a group of error equations 
are built. Then the Unknown parameters of formula (1) are 
found by a least squares adjustment process. 
For example, take affine transform 
However, we cannot directly detect them using these two 
characters above, in fact. Because, if we want to validate 
whether these two characters come into existence, we must fit a 
straight line with the chain firstly. In this way we blindly 
suppose that all points in the chain are from one straight line. In 
practice straight line segments are often embodied in parts of 
the whole chain. In this condition, we cannot rightly divide 
straight line parts from the whole chain, using these two 
characters. As shown in figure 3, the solid line represents a edge 
chain code, which assembled by a straight line segment AC 
and a curve CB. The dashed line represents the fitted straight 
line. This fitted straight line satisfies the two characters, but it is 
not a right division of straight line segment AC ■ 
x =a Q +a x x +a 2 y 
y d = b 0 + h x x s + b 2 y s 
as coordinate transform form, we need to find 6 transform 
parameters. Every pairs of corresponding straight lines can give 
2 error equations, so we need 3 pairs of corresponding straight 
lines at least. They should be distributed uniformly in the whole 
image. In addition, there is a connotative basic request: each 
two pairs should not be parallel if there are only 3 pairs of 
corresponding straight lines. 
3. AUTOMATIC EXTRACTION OF STRAIGHT LINE 
SEGMENT 
Traditional straight line extraction methods include Hough 
transform [Hough 1962], which transforms binary image 
function to straight line parameter description. The maximum 
values in parameter space are the straight lines in image space. 
However, because of poor positioning capability, Hough 
transform is not a good method to extract control straight lines 
from image. [Zhang Hongwei, 2004] adopts a “feature 
extraction and straight line tracking” process to extract straight 
line segments from image. Firstly the prominent edges are 
extracted using Canny operator (Canny 1986). Then the edges 
are thinned and tracked to get edge chains with one single pixel 
width. At last edge chains are separated and merged until they 
can be fitted as straight line segments. 
To act as control objects of image registration, straight line 
segments must be the prominent features in both reference and 
source image. In this article, two characters of the prominent 
straight line segment are proposed. They are 
(1) The length of the straight line segment must be above a 
threshold value N , and 
(2) The vertical distance from every point in the chain to the 
fitted straight line must be below a threshold value A . 
B 
Figure 4. Straight line segment detection with a link line 
between head and tail of edge chain 
As shown in figure 4, deriving from the two straight line 
segment characters, if a straight line segment is embodied in the 
edge chain, a line AC can represent this straight line segment. 
Here AC is a link line between head and tail of the straight line 
part in the edge chain. Using this rule, we design a straight line 
segment detection process. In this process, the fitted straight 
line is replaced by line AB, a link between head and tail of 
the whole edge chain. Then all points in edge chain are checked 
to validate whether these two characters are met. If both two 
characters are met, the output straight line will be fitted with all 
points in edge chain. Otherwise, the edge chain is divided into 
two parts AD and DB. Here D is the farthest endpoint from 
straight line AB . Then the “detecting and dividing” process is 
performed with these two edge chains. This process is repeated 
until all the edge chains divided into short chains. That is, 
except the edge chains which have fitted to straight line, all 
others have pixels less than N , thus the two characters will be 
not met anymore. 
The algorithm is described as follows: for each chain code of 
edge, 
(1) This chain is abandoned and the process turns to the next 
chain, unless the number of pixels in it is above the 
threshold value N; 
(2) This chain is abandoned and the process turns to the next 
chain, unless the length of AB, a link line from the head