An image histogram is a graphic representation of the frequency
counts of all allowable pixel intensities. Figure 2.1 shows a
sample of an image with a skewed histogram.
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Figure 2.1 A sample image with a skewed histogram (poor intensity
distribution)
Since the human eye is sensitive to contrast rather than absolute pixel intensities, we would perceive less information from an image with poor intensity distributions than from the same image with better intensity distributions. Images with skewed distributions can be helped with histogram equalization (Figure 2.2). Histogram equalization is a point process that redistributes the image's intensity distributions in order to obtain a uniform histogram for the image. Histogram equalization can be done in three steps [1]:
Figure 2.2 shows the normalized sum of the image in Figure 2.1,
the histogram-equalized image, and its histogram. Note that the
resulting histogram is not truly uniform, but it is better distributed
than before. Truly uniformed histograms for discrete images are
difficult to obtained because of quantization.
| intensity | sum | normalized sum |
| 0 | 1 | 1/16*5=0.31255 |
| 1 | 8 | 2.5 |
| 2 | 12 | 3.75 |
| 3 | 14 | 4.375 |
| 4 | 15 | 4.6875 |
| 5 | 16 | 5.0 |
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Figure 2.2 A histogram-equalized sample with histogram and normalized
sum
Listing 2.1 shows a MATLAB implementation of the histogram equalization
function. This implementation is a table-lookup implementation.
histogram_equalize - histogram-equalizes an input image.
SYNOPSIS
histogram_equalize(input_file_name, output_file_name)
DESCRIPTION
histogram_equalize performs histogram equalization on an
input image. It reads the image from the input file, computes
the histogram, calculates the normalized sum, transforms the input
image to an output image, and writes the output image into the
output file. . The input image can be in Windows Bitmap (bmp),
Hierarchical Data Format (HDF), Joint Photographic Experts Group
(JPEG), Windows Paintbrush (PCX), Tagged Image File Format (TIFF),
or Window Dump (XWD) format. The output file is in TIFF format.
EXAMPLES
histogram_equalize('BIRDGIRL.TIF', 'he_bg.tif')
This example (Figure 2.3) histogram-equalizes BIRDGIRL shown in Figure 1.1(a).
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| a. Histogram_equalized BIRDGIRL | b. Histogram of histogram_equalized BIRDGIRL | c. Histogram of original BIRDGIRL |
Figure 2.3 Histogram-equalized BIRDGIRL and its histogram
