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Given a standard image, we call all the other images to be 
compared with the standard candidate images. We denote OB the 
range of a standard image (the solid lines shown in Fig. 2), BA 
the sill and [JAOB to be 0 . Elongating BA and intersecting with 
another semivariogram curve of another image (the candidate 
image, shown in Fig. 2 with imagery lines), denoting C the 
intersect point. Let [JCOB be A (not shown in the figure), then the 
bigger the difference of the two images (the standard image and 
the candidate), the bigger the difference of angle 0 and P. Let: 
. tang BA 
A tan# BC 
  
(9) 
then p is a parameter with no metric unit. If the more the 
aberration of p from 1, the bigger the difference between the 
standard image and the candidate, otherwise, the more similar 
between the standard and the candidate. If p=1, that means the 
standard image and the candidate are actually the same. By this 
way, the parameter p can be a good candidate for measuring the 
similarity between two images. Compared with image similarity 
measurements such as derived from histogram intersection, this 
parameter has powerful ability to describe image structure 
differences which is strongly related with the properties of 
semivariogram. If different semivariograms of different 
orientations are calculated both for standard image and candidate, 
and calculating different value of p corresponding to these 
orientations, then the degree of similarity between standard 
image and candidate can be determined by giving a range of 
threshold value, for instance, 0.7<p<1.3. Besides, this parameter 
has at least three merits listed as follows: 
(1) the sensitivity to structure difference of a data set. In 
literature of spatial statistics, there are lots of detailed 
discussions on how the semivariogram can describe 
structure of a data set. Generally speaking, semivariogram 
can indicate structure differences accurately and effectively 
so that parameter p inherits this property; 
(2) the highest complexity of calculation of semivariogram is 
O(N?), which is lower than any one of the four similarity 
distances proposed by Di Gesu; 
(3) even if the standard image and the candidate are very 
different in illumination condition, there still have 
differences in parameter p, if only there are structure 
differences. That is, this parameter is robust to illumination. 
This is because the calculation of semivariogram is a 
procedure similar to sliding average in one dimensional 
space with a variable step h. Besides, the parameter © 
does not require the standard image and the candidate has 
the same size, while all the four similarity distances defined 
by Di Gesu (1999) require the same size of the standard and 
candidate images. 
4. APPLICATION 
This application comes from the railway department of China. 
Almost all big railway stations in China have special workers to 
check wheels of a train while it stops at the station in order to see 
whether the brake system of the train works well. If there are any 
problems, they must report to related divisions of the station at 
once to solve the problem before the train leaves. The whole 
procedure is finished manually by workers and potential risks 
existing if a worker happens to miss one or two wheels which 
have problems of their brake systems. Automatically checking 
the wheels is a task of great value. 
Ifa CCD camera is used to capture train wheels when the train is 
coming and adopting digital image processing techniques to 
recognize brakes (shown in Fig. 3), then the whole procedure of 
brake system checking will be automatic. If the speed capturing 
train wheels of the CCD camera is 6 frames per second, then 
more than 1,000 digital images will be captured. However, most 
of them are useless, since they are not the pictures of train wheels. 
So the first step of automation is picking out the useful images 
(the images that are train wheels) from all the image captured by 
the CCD camera. 
  
  
brake of a train wheel 
Fig. 3 typical useful image of train wheel 
This is actually a problem of image retrieval. Because train wheel 
has typical geometric features, recognizing these features and 
employing shape-based image retrieval technique becomes the 
first choice. However, it is a non-uniform motion when a train is 
coming to a station, which leads to geometric distortions of these 
features. This makes curve extraction algorithms such as Hough 
Transform have much more computational complexities than 
usual, which are actually un-operational. If area-based image 
matching between a standard image and a candidate is used, it is 
operational as for computational complexity, but it is too 
sensitive to illumination condition. Another situation that must 
be considered is motion blurring as shown in Fig. 4. All the 
existing approaches for motion image analysis lose their 
effectiveness due to the non-uniform motion of the train when it 
is coming to the station. A new method must be used in order to 
solve all these problems. 
  
Fig. 4 typical image with motion blurring 
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