Gamal Seedahmed 
  
   
Fig. 4: The detected peaks for the Inner and Outer Circles respectively. 
  
  
  
  
  
  
  
  
  
  
Location | Radius in pixels | i center | j center | Traced Analytical Success 
Perimeter Perimeter 
UL Inner 26 214 258 156 163.38 Yes. 
UL Outer 33 214 257 198 207.37 Yes. 
LL Inner 26 405 284 158 163.38 Yes, 
LL Outer 33 405 284 185 207.37 Yes. 
UR Inner 26 162 177 127 163.38 Yes. 
UR Outer 33 162 177 183 207.37 Yes. 
LR Inner 26 132 280 143 163.38 Yes. 
LR Outer 33 132 279 203 207.37 Yes. 
  
  
  
  
  
  
  
Table 1:The results of HT for the FM with their pixel tracing. 
Results of Precise Localization: 
  
  
  
  
  
  
  
  
UL UR 
j=257.245 i=213.872 j-176.974  i-161.98 
Dispersion Matrix: Dispersion Matrix: 
0.002 —1.12-5 0.003 4.5¢-5 
-1.1e-5 0.002 4.5e—5 0.003 
Redundancy=352 Redundancy=308 
c? - 0.356 o, =0.551 
LL LR 
j=284.007 i=405.034 J=279.362 i=132.275 
Dispersion Matrix: Dispersion Matrix: 
0.003 4.5¢-5 0.002 1.0e-5 
45e-5 0.003 1.00-5 0.002 
Redundancy=341 Redundancy=344 
  
  
  
  
  
  
The identified and precisely localized FM are used with their calibrated FM to determine the affine 
transformation parameters, which relate the pixel, coordinates with the photo coordinates. The affine 
transformation can be represented by: 
X pires =a, +b X Calibra * Cu earned + €, 
(4) 
You =a,+b,X Calibrated : + Ca Ÿ catioraed + € y 
The above representation of the affine transformation will allow treating the calibrated FM as error free 
observations, and the stochastic property of the model can be handled via Gauss-Markov model. 
  
828 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.