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crack vectors and precise width can be 
generated. At the end of crack measure- 
ment processing, coordinates of crack 
vectors and scale of width are rectified 
using to the fiducial points arranged on 
concrete. 
Crack measuring process is divided into 
five stages; mapping crack vectors, 
thresholding, noise reduction, detailed 
positioning and measurement of crack 
width (see Fig. 6). 
À previous processing of crack measuring on a coarser image 
Coarse crack 
vectors and 
width 
  
Finer crack 
vectors are 
generated and 
width is 
measured. 
  
  
  
Finer crack 
vectors and 
width 
  
+ 
À following processing of crack measuring on a finer image 
Fig.5. A schema of hierarchical crack measuring 
Start 
(rm 
Mapping crack vectors | 
I 
Thresholding = 
I 
  
  
  
  
  
  
I 
Detailed positioning | 
I 
  
  
  
| 
| 
| Noise reduction | 
| 
| 
Measurement of crack width | 
  
  
repeat until finishing 
on the original image 
| Rectification of scale | 
I 
End 
  
  
  
Fig.6. The flow chart of hierarchical 
crack measuring algorithm 
     
  
    
    
   
    
       
  
  
   
   
   
  
  
    
     
  
   
    
   
   
   
     
  
  
   
  
    
   
  
  
   
  
  
   
   
   
    
    
    
   
   
  
   
    
   
  
   
    
   
3.1 Mapping crack vectors 
Each vector of cracks is mapped onto the 
image one step finer than the present 
image. Because the ratio of resolution 
between these images is 2:1, the location 
of mapped vector has an ambiguity in 
area of 2x2 pixels (see Fig. 7). 
À crack vector on a present 
image 
Àn ambiguity in area of 2 X 2 
pixels on a one step finer image 
Fig. T. Ambiguity of mapping 
3.2 Thresholding 
A threshold value is determined by the 
method based on discriminating and least 
squares criteria suggested by Ohtsu 
(1980), following which the finer image 
is thresholded into a binary image. 
A threshold value of each crack vector is 
calculated in an elliptical target shown 
in Fig. 8, which the major axis of the 
ellipse is directed along the crack. In 
order to accomplish an adequate  calcula- 
tion, the length of the minor axis is 
determined to be twice or three times of 
the crack width which has been computed 
on the present image. 
It is noted that the initial crack width 
on the coarsest image can be determined 
from the number of execution times re- 
quired in thinning process. 
   
  
           
       
    
A 
Lr 
À crack on a finer image 
Elliptical target in which 
threshold is computed 
A length varies in propotion 
to the crack width computed 
in previous processing. 
A 
EO © 
  
    
     
e 
_ 
A crack vector 
Fig. 8. An elliptical target for thresholding 
3.3 Noise reduction 
Fig. 9 shows an example of small isolated 
holes in the thresholded area. These 
holes, which usually prevent detailed 
positioning of crack vectors and precise 
measurement of crack width, must be 
filled.