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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004 
  
3.5 Positive-negative recognition 
During the localization stage, algorithm recognizes if the 
extracted patch is positive or negative. [n case of negative, the 
patch converts to positive. The values of grey value correlation 
matrix help us to determine if mask is positive and image is 
negative so the values of grey value correlation matrix become 
negative. In case that mask and patch are positive, the matrix of 
grey value correlation has positive values. 
3.6 Estimation of the transformation parameters 
Now the accurate positions of fiducial marks were known and 
the position of which in photo coordinate system are available 
through camera calibration file. To establish a geometric 
relationship between pixel and photo coordinate system, 
projective transformation is used to achieve this goal. 
At least exact position of four out of eight fiducial marks should 
be known (Eq.1) 
Cox bye 
Ee (1) 
G,X Fb. y +1 
(Xd 5 y c, 
ax hy 
where: 
[a, b, c] — Transformation parameters 
[x > | = Photo coordinates of fiducial marks 
[x] = Pixel coordinates of fiducial marks 
3.7 Localization 
From various methods used to localize the fiducial mark, we 
chose two methods which help us to obtain a better accuracy as 
follow: 
3.7.1 Cross Correlation Function (CCF) 
In this method, a small patch with a search area of 512 by 512 
pixels is read from the original image called (f). Template of 
fiducial mark (w) is conducted to search over the top level of 
pyramid of extracted patches until the best match between the 
template and a certain patch is found. Template(w) moves over 
the search window one by one pixel forward systematically and 
in every step normalized correlation coefficient is calculated 
which indicated the best match between (w) and (f) when value 
of (r) is maximum as shown in Eq.2. 
Un 
UA 
  
  
  
  
  
  
  
  
  
  
f(x ,y) X 
— 
A 
O 
M 
W(x ,y) 
Vy 
Y 
N 
Figure 6. Arrangement for the obtaining of f(x, y) and w(x, y) at 
a given point 
  
YMA (y) - [wx-my- n)-w| (2) 
: xy 
m n, n) = ; 
.o—2 x 
xy x y 
Where: 
W = the average value of the pixels in w(x, y). 
f = the average value of f(x, y) in the region coincident with 
the current location of w 
r(m, n) - normalized correlation coefficient at a given point 
of (m, n) 
The summations are taken over the coordinates common to both 
f. and W . The correlation coefficients are scaled in the range 
of -1 to 1. In case of the best matching, the number would be 1. 
3.7.2 Binary Cross Correlation Function (BCCF) 
This method is similar to the previous one with the difference of 
using binary patch and template windows. What is important is 
how to estimate the amount of a suitable threshold for this 
purpose. 
3.8 Precise measurement 
In this Paper we used two more accurate methods as follow: 
3.8.1 Interpolation and surface fitting (ISF) 
In this method, we fit a bilinear surface (Eq.3) on the 
approximate pixel position obtained from previous stage and its 
surrounding. 
The precise position with sub-pixel accuracy will be gain by 
derivation of the bilinear surface as shown in Fig. 7.