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Byung-Uk Park 
  
Binary images shown in Figure 4 were used as a basic entry are for the Hough transform. In this research we 
used only line features to estimate the center of the fiducial marks. Figure 4(c) shows some noises compared to other 
binary images. With proper selection of 6, the noise element was able to be removed and Hough transform was applied 
successfully accordingly. 
Two peaks represented in accumulator array are mapped into two straight lines. The final results of Hough 
transform are shown in Figure 5. We calculated the intersection of the lines and obtained the center location of the 
fiducial marks. Intersections of extracted fiducial marks using Hough transform are given in Table 2. We compared the 
central location of the automatically detected fiducial marks with manually estimated location. Automatically extracted 
central location of fiducial marks falls inside the pixel of the manually selected location. 
JAEII 
(a) (c) (d) 
Figure 5. The final result of Hough transform 
    
  
  
  
  
  
  
  
  
  
  
  
Crossing point Crossing point 
Fiducial mark | linear equation in image patch In full scene 
X Y X Y 
(]) = 
Fig. 5(a) a 25.500 25.500 167.500 | 212.500 
(2)y=-x+51 
(1 ) == 
Fig. 5(b) set 28.000 28.000 | 5215.000 | 234.000 
(2) y=-x+56 
Dv= x. 
Fig. Sleds) fonts ed 27.500 26.500 | 148.500 | 5259.500 
Qy=-x+54 
(Dvz x- 
Fig. 5(d) Lyng los. ^a5,500 24.500 | 5194.500 | 5279.500 
£y--X- 54 
  
  
  
Table 2. Intersections of extracted fiducial mark through Hough transform. 
We performed affine transformation to relate the calibration data with the location of automatically calculated 
fiducial marks. Parameters of affine transformation and the results of interior orientation are shown in Table 3 and 
Table 4, respectively. 
  
  
  
  
  
  
  
  
  
  
  
  
  
Fiducial Calibrated data of fiducial Image coordinate. 
mark Bark 
x(mm) y(mm) Column Row 
Fig.5(a) -106.000 106.000 167.500 212.500 
Fig.5(b) 105.996 105.999 5215.000 234.000 
Fig.5(c) -106.001 -106.004 148.500 5259.500 
Fig.5(d) 105.999 -105.999 5194.500 5279.500 
Parameters of affine transformation Equations for affine transformation 
az 0.0420 b= 0.0002 Xeaxeby4c 
€cz-113.08782 ds 0.0002 Ysdxtey f 
e= -0.04201 f=114.91251 
  
Table 3. Parameters for affine transformation 
  
  
Adjusted fiducial coordinates 
Residuals in fiducial coordinates 
  
-106.0168 
106.0142 
0.0168 
-0.0142 
  
106.0128 
  
105.9848 
  
-0.0168 
  
0.0142 
  
  
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 
695