# Local enhancement using histogram statistics

This method is used to enhance details over small areas in an image. The procedure is to define a square or rectangular neighborhood and move the center of this area from pixel to pixel. At each location, the histogram of the points in the neighborhood is computed and either a histogram equalization or histogram specification transformation function is obtained. This function is finally used to map the gray level of the pixel centered in the neighborhood. The center of the neighborhood region is then moved to an adjacent pixel location and the procedure is repeated. Since only one new row or column of the neighborhood changes during a pixel-to-pixel translation of the region, updating the histogram obtained in the previous location with the new data introduced at each motion step is possible. This approach has obvious advantages over repeatedly computing the histogram over all pixels in the neighborhood region each time the region is moved one pixel location. Another approach used some times to reduce computation is to utilize non-overlapping regions, but this method usually produces an undesirable checkerboard effect. 3×3 neighborhood about a point (x,y) in the image
We consider two uses of the mean and variance for enhancement purposes. The global mean and variance are measured over an entire image and are useful primarily for gross adjustments of overall intensity and contrast. A much more powerful use of these two measures is in local enhancement, where the local mean and variance are used as the basis for making changes that depend on image characteristics in a predefined region about each pixel in the image. ……………….(i) ……………….(ii)

Let (x, y) be the coordinates of a pixel in an image, and let Sxy denote a neighborhood (subimage) of specified size, centered at (x, y).From (following equation) the mean value mSxy of the pixels in Sxy can be computed using the expression : ……………….(iii)

where rs, t is the gray level at coordinates (s, t) in the neighborhood, and p(rs, t) is the neighborhood normalized histogram component corresponding to that value of gray level. Similarly, from (Equation 2), the gray-level variance of the pixels in region Sxy is given by ……………….(iv)

The local mean is a measure of average gray level in neighborhood Sxy, and the variance (or standard deviation) is a measure of contrast in that neighborhood. An important aspect of image processing using the local mean and variance is the flexibility they afford in developing simple, yet powerful enhancement techniques based on statistical measures that have a close, predictable correspondence with image appearance.

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