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        12.1.3 Quantization of Gray-Level Value
        To represent  an analog  image by discrete gray-level  values is called quantization
        of  the image. For example, when the brightest  gray-level value is  "000"  and the
        darkest is "111," this is called a quantization of eight  levels.  In other words, it is
        eight  gray-scale representations.  Conventionally, 64-256  gray-level representa-
        tions are used for quantization.


        12.1.4 Gray-Scale Binary Image Display

        If the number of pixels in a region  of a gray-scale  image is fixed, then the  display
        with binary data, 0 or  1, will be represented  by the least amount of data. The fea-
        tures of an image can be preserved by proper conversion to its binary image. When
        the image is binary data, it can be processed easily.



        12.1.5 Threshold  Processing
        There are a variety of methods for obtaining binary data. One of the easiest  uses a
        gray-level histogram.  Consider  an image composed  of an object and a  background.
        In the density histogram,  the gray-level value where  there is a large  change  in
        the number of pixels is called the threshold. (An example is shown in upcoming
        (Figure  12.4.)
            In the second method for obtaining binary data, when the number of pixels of
        an object is known and the gray level  of the object is quite low, the  threshold  is
        obtained from the ratio P of the number of pixels of the object to the total number
        of pixels in the image.



        12.2 IMAGE  DISPLAY

        12.2.1  Density Distribution

        The distribution  of gray-level values in an image with MxN  pixels  is called  the
        density  histogram. It is not good for image processing  if the density distribution  is
        biased.  Therefore  it  is  necessary  to  make  the  distribution  uniform by changing
        either  the light  source  or the direction  of the lens.



        12.2.2 Density  Transformation
        In  order  to get a good-quality  image,  a full-scale  gray-level  display  is desirable.
        To achieve this, the density transformation method is used. As shown in Figure  12.2,
        density transformation is achieved via line transformation.
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