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properly by introducing the weight : 
where © is the standard deviation and k a proportionality 
constant. 
Then the least squares criterion becomes: 
OQ = wi up +waotug+....... +WN*uN = min 
where u; are observation residuals , 
and the solution vector is given by : 
X - (A*W*A) I«(At*W*F) (4) 
The standard deviations of the ( x;,y:) are the elements of : 
(A W*A)! 
where À is a N by 1 matrix of the coefficients of the weights of 
the observations, W a diagonal weight matrix, and F an N by 1 
matrix of constants indicating linearity of the condition 
equations. 
Equation (4) is iterated until the desired accuracy is achieved. In 
any iteration the initial value of X was taken from the previous 
iteration. 
Experiments have been carried out for the above described 
approach to evaluate the performance of the HT under various 
conditions such as: variation of angle of lines, length of line 
segments, number of lines in the target, noise contamination, 
and quantization of the parameter space. It is found that for a 
noisy image the best accuracy is given by four equally spaced 
lines with normal distance quantization equal to one, and angle 
quantization equal to one degree. 
The main advantage of the proposed method for target detection 
and accurate measurement is that the whole procedure is totally 
automated. The target detection can be performed quickly and 
safely and then the center of the circular target can be found in 
the image either as the center of the corresponding ellipse-circle 
or as the intersection of four equally spaced diameters of the 
circle target. 
The method works well even under the most noisy environment. 
No limitations have been observed. Practical experiments 
showed that the standard deviation of the target center position 
in repetitive image acquisitions with different conditions of 
illumination was in the subpixel level. 
5. CONCLUSIONS 
A target detection method based on the Hough Transform and 
utilizing a white circle with four diagonal black lines in a black 
background is proposed. The method provides automated and 
safe target detection even in the most inconvenient images 
(noisy,interrupted). It works in an gradient image and the 
accuracy of the target detection is of subpixel magnitude. 
The purpose of the recent paper is to underline to the 
photogrammetrists the existence of a powerful tool named 
Hough Transform which in a digital image environment can 
offer a lot in the pattern recognition process. Except for the 
253 
described target detection application of the Hough Transform, 
work is currently underway by the authors in applying HT in 
image matching techniques. 
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