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orm has 
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nine the 
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method 
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er space 
Byung-Uk Park 
  
y=ax+b (1) 
b = -xa + y (2) 
Straight line can be represented as equation (1) and (2). However, this parametric model has some difficulties 
in the representation of vertical straight line, because the parameter tends to go infinity. To overcome this difficulty, 
Duda and Hart (1972) proposed a polar representation of a straight line. 
p=xcos6+ysin 60 (3) 
À A 
6 
  
  
Figure 1. Representation of polar coordinate system 
Equation (3) describes a line having direction angle 0 at distance p from the origin, as can be seen in Figure 1. 
A straight line passing through the point (x,, y;) represents a sinusoidal curve p = x,cos 0 + y,sin 0 in the parameter 
space (p, 0). Collinear points (x,, y,) on the binary image space correspond to crossings of sinusoidal curves on the 
parameter space. Consequently, a similar algorithm to the one described in Figure 1 can be utilized by adapting the 
model (3) instead of equation (1). The range of the parameters (0, p) is below for an image of size M, x M,. 
0«p« Mi*M) (4) 
0<6<180 (5) 
Hough transform for locating the fiducial mark has been performed as the following procedure (Figure 2). 
Input of binary image 
Y 
Size determination of 
accumulator array 
v 
Mapping into parameter space 
through Hough transform 
v 
Determination of threshold value 
Y 
Implementation of 
inverse Hough transform 
Y 
Result out 
poor 
good 
Y 
The end 
Figure 2. Flowchart of Hough transform procedure. 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 693