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156     INTELLIGENT COMMUNICATION SYSTEMS


              ( i ~ l , 7 - l )      ^22^1              (i+1,7-D
              0"~  1, 7)             (',  7)            (i+1,7)

                                        7
              (i-1,7+D        i      0', + D       i    (i+1,7+D
         FIGURE  12.7  3 x 3 region for smoothing.


        12.3.1  Space Filtering
        This method has the following objectives:  (1) to eliminate noise from  the source
        image, called smoothing, and (2) to detect features of the image such as contour
        and  direction  from  the  source  image.  To  achieve  these  objectives  we  use  the
        Laplacian and gradient operations.
            When it is difficult  to obtain gray-level values accurately because a high fre-
        quency has been introduced into the video  signal, a smoothing  operation  is per-
        formed, A mean value is calculated for nine pixels, from pixel (i -  1, j -  1) to pixel
        (/ +  1, j  + 1), and this value is assigned to a new gray level (see Figure  12.7). The
        formula  is as follows:









        where  T(i,f)  is the coefficient of g(i,j).  This means that f(i,  f)  is the summation
        from g(i-l,j-l)  to g(i + lj+i)  divided by 9. The gray-level values g(i -IJ-1),
        g(ij  -  1), g(i +IJ-  1), g(i -  I,/), g(i + I,/), g(i -  1,7 + 1), gdJ  + 1), gd +1,7 + 1)
        are used to calculate/(i, 7) in space filtering.
           In  space filtering, a mean value is used for/(/,/). Another method involves
        decreasing  the value of the coefficient as the distance from g(i, j)  increases. One
        example is shown in Eq. (7).







           In general, T(i,j)  is described  as follows:






        Here, w n is the coefficient of the gray level.
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