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is associated with the exposure when the picture is taken. Brightness adjustments can improve viewing ability of the darker or brighter areas by increasing or decreasing the luminance value of each pixel. Since the modi cation of brightness changes every pixel in the image, the entire image will become brighter or darker. Saturation may occur with the brightness adjustment. Changing brightness of an image will not affect the contrast of the image. Contrast can be adjusted by varying the luminance value of each pixel. The adjustment to the contrast may also result in saturation if the pixel values reach the limit. Histogram equalization uses a monotonic nonlinear mapping process to redistribute the intensity values of an image such that the resulting image has a much uniform distribution of intensities. Histogram equalization may not work well on all images because the redistribution does not use the priori knowledge of the image. Sometimes, it may even make the image worse. However, histogram equalization works well especially for ne details in the darker regions or for B&W images. The histogram equalization consists of the following three steps: 1. Compute the histogram of the image. 2. Normalize the histogram. 3. Normalize the image using the normalized histogram.
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Example 15.6: This example computes the histogram of a given image and equalizes this image
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based on its histogram. Figure 15.10 shows the original image, the equalized image, and their histograms using the MATLAB script (example15_6.m). As shown in the gure, the original image is very dark because it was taken in the evening without using ashlight. Most of the pixels are concentrated in the lower portion of the histogram as shown in Figure 15.10(c). The viewing quality of this image can be improved by increasing the contrast using histogram equalization. Figure 15.10(b) shows that most of the dark background scene has been clearly revealed. Figure 15.10(d) is the histogram of the equalized image. The histogram of the equalized image redistributes the pixel values more evenly by adjusting the contrast level. Example 15.6 shows that the histogram equalization is an automated process to replace the trial-anderror manual adjustment. It is an effective way to enhance the contrast. However, since the histogram equalization applies an approximated uniform histogram blindly, some undesired effects could occur. For example, in Figure 15.10(b), the facial details are lost after the histogram equalization although the surrounding scene is enhanced. This problem may be overcome by using an adaptive histogram equalization, which divides the image to several regions and individually equalizes each smaller region instead of entire image. To reduce the artifacts caused by the boundaries of the small regions, additional smooth process should be used.
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15.7 Image Filtering
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Many video and image applications use 2-D lters for image processing. If the input to the system is an impulse (delta) function (x, y) at the origin, the output is the system s impulse response. When the system s response remains the same regardless of the position of the impulse function, the system is de ned as linear space-invariant system. A linear space-invariant system can be described by its impulse response as Figure 15.11. An image processing system is a 2-D system, and thus an image ltering uses a 2-D lter. Similar to a 1-D FIR ltering, the image ltering is a 2-D convolution of the lter kernel with the image, which can
INTRODUCTION TO DIGITAL IMAGE PROCESSING
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5000 4000 3000 2000 1000 0 0 50 100 150 200 250 (c) Histograms of the original image.
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5000 4000 3000 2000 1000 0 0 50 100 150 200 (d) Histogram of the equalized image. 250
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Figure 15.10 Image equalization based on its histogram: (a) original image; (b) equalized image based on histogram; (c) histograms of the original image; and (d) histogram of the equalized image
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x(i, j)
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h(i, j)
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y(i, j) = x(i, j)* h(i, j)
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A linear space-invariant 2-D system
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An example of 3 3 image convolution: (a) image block; (b) lter kernel
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be expressed as
N 1 M 1 i=0 j=0
y(n, m) =
h(i, j)x(n i, m j),
(15.13)
where M and N are the width and height of the 2-D lter, respectively. Figure 15.12 shows an example of 3 3 image convolution expressed as y(4, 4) = h 0,0 x(3, 3) + h 0,1 x(3, 4) + h 0,2 x(3, 5) +h 1,0 x(4, 3) + h 1,1 x(4, 4) + h 1,2 x(4, 5) +h 2,0 x(5, 3) + h 2,1 x(5, 4) + h 2,2 x(5, 5) where the image data is denoted as x(n, m), and the lter kernel is denoted by h i, j . Image ltering can affect the digital image in many ways, such as reducing the noise, enhancing the edges, sharpening the image, and blurring the image. Image ltering can also generate many special effects for the digital photos. Linear lters are widely used in image processing and editing. Linear smoothing (or lowpass) lters are effective in reducing noises. The common noises in images are Gaussian noise introduced by camera s image sensors, impulse noise caused by sudden intensity change in white values (may also result from bad image sensor), and B&W high-frequency noises called salt and pepper noises. The linear lters usually use weighted coef cients. Typically, the sum of the lter coef cients equals to 1 in order to keep the same image intensity. If the sum is larger than 1, the resulting image will be brighter; otherwise, it will be darker. Some commonly used 2-D lters are the 3 3 kernels summarized as follows: 0 0 0 = 0 1 0 . 0 0 0 1 1 1 1 1 1 1 . = 9 1 1 1