width on fine image can be transformed 
into line-edge on the coarse image, and 
hence the cracks can be detected with a 
single spatial filter in the hierarchy. 
From this point of view, the rate of 
reduction which is suitable to detect the 
cracks. ranging: from 0.1 to. 3.0 mm: in 
width can be estimated at 1/30. 
2.1.1 Line reserving smooth filter In 
course of reduction, however, misdetec- 
tion of fine cracks arise from various 
stains which are often observed on  con- 
crete surface, such as mud, small holes, 
exfoliation and so on. The reason for the 
misdetection is that the pixels  corre- 
sponding to such stains have rather high 
value than the pixels on fine cracks and 
work as noise. In order to reduce mis- 
computation, the original image is pre- 
processed with a line reserving smooth 
filter shown in Fig. 2. A certain noise 
whose length is less than the size of 
filter can be smoothed in the preprocess- 
ing, while the cracks seem to be linear 
structures still remain. 
  
And furthermore, to prevent an increase 
in undetectable fine cracks affected by 
residual noise, a series of images is 
gradually reduced into 1/2 size step by 
step till the coarsest image which  reso- 
lution is intended to detect the target 
cracks (see Fig. 3). 
  
  
  
1 
8 A 2 
7 3 
6 4 
5< >5 
4 6 
7 
2 Y 
1 8 
  
  
  
On each point of an image, a line reserving 
smooth filter finds out the maximum of mean 
values on each line of 8 directions. 
Fig.2. A line reserving smooth filter 
The coarsest image 
Reduction in size 
by selecting 
maximum value of 
pixels 
  
The original fine 
image 
  
  
Fig.3. A series of images structured hierarchically 
    
2.2 Edge detection 
After generating a series of images, edge 
detection is performed on the hierarchi- 
cal images. The edge detection is divided 
into five stages; line-edge filtering, 
thresholding, noise reduction, thinning 
and vectorization (see Fig. 4). 
Start 
1 
Line-edge filtering 
1 
  
Thresholding 
I 
  
I 
Thinning 
j 
  
| | 
| | 
| Noise reduction | 
| ] 
| | 
Vectorization 
Ï 
End 
Fig. 4. The flow chart of line edge detection in 
hierarchical edge detecting algorithm 
2.2.1 Line-edge filtering Suzuki 
(1985)'s Directional Contrast Filter is 
convoluted on the image to detect  line- 
edge ranging from 1 to 5 pixels in width. 
  
2.2.2 Thresholding A threshold value 
is determined by computation of an aver- 
age on the filtered image, following 
which the image is thresholded into a 
binary image. The pixel of value more 
than the threshold is regarded as a part 
of pixels on cracks. 
2.2.3 Noise reduction A small lump 
of pixels is removed as a noise, which 
length and area to be eliminated are 
previously determined. 
2.2.4 Thinning A linear chain of 
pixels which is prospected to construct a 
crack is skeletonized to determine the 
position of a crack. 
243235 Vectorization A series of 
coordinates of each chaining pixel which 
represents position vector on the binary 
image compose a set of crack. In the 
vectorization, the coordinates are calcu- 
lated by tracing along the skeleton. And 
then, several sets of crack which are 
extracted from a finer image are combined 
with the sets from the coarsest image. 
While the combination is carried out, the 
sets from a finer are weighted. 
S.HIERARCHICAL CRACK MEASURING ALGORITHM 
The crack vectors extracted from the 
coarsest image are positioned roughly 
rather than from the fine image, and 
hence they lead to rough-measurement of 
crack width. 
Detailed positioning and precise measure- 
ment can be achieved by means of mapping 
coarse vectors onto a finer image. The 
mapping operation with measuring crack 
width is carried out step by step on each 
hierarchical image shown in Fig. 5, which 
turns back the way of image reducing 
process. As the execution is finished on 
the fine original image, the detailed