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© 2002 R. C. Gonzalez & R. E. Woods

Chapter 4Image Enhancement in the

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2002 Gonzalez & Woods

2003 Spring, Digital Image Processing Softcomp.ee.ntou.edu.tw



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EXAMPLE 4.9: High-frequency emphasis filtering. Transfer function given by

Hhfe(u,v)=a + bHhp(u,v) (4.4-20)

where a 0 and b > a. Typical values of a are in the range 0.25 to 0.5 and typical values of b are in the range 1.5 to 2.0. With reference to Eq. (4.4-17), we see that high-frequency emphasis reduces to high-boost filtering when a = (A-1) and b = 1. When b > I, the high frequencies are emphasized, thus giving this procedure its name.

Figure 4.30(a) shows a chest X-ray with a narrow range of gray levels. Our main objective is to sharpen the image. X-rays cannot be focused in the same manner that lenses are focused, and the resulting images generally tend to be slightly blurred. Since the gray levels in this particular image are biased toward the dark end of the gray scale, we also take the opportunity here to give an example of how spatial domain processing can be used to complement frequency domain filtering.

Figure 4.30(b) shows the result of highpass filtering using a Butterworth filter (see p.183, Eq.4.4-3) of order 2 and a value of D0 equal to 5 of the image vertical dimension,



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Highpass filtering is not overly sensitive to this parameter, as long as the radius of the filter is not so small that frequencies near the origin of the transform are passed. As expected, the filtered result is rather featureless, but it shows faintly the principal edges in the image. The advantage of high-emphasis filtering (with a = 0.5 and b = 2.0 in this case) is shown in the image of Fig. 4.30(c). Although the image is still dark, the gray-level tonality due to the low frequency components was not lost.

As indicated in Section 3.3, an image characterized by gray levels in a narrow range of the gray scale is an ideal candidate for histogram equalization. As shown in Fig. 4.30(d), this indeed was an appropriate method to further enhance the image. Note the clarity of the bone structure and other details that simply are not visible in any of the other three images.

The final enhanced image is a little noisy, but this is typical of X-ray images when their gray scale is expanded. The result obtained using a combination of high-frequency emphasis and histogram equalization is superior to the result that would be obtained by using either method alone.



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Homomorphic filtering (同形濾波 ) Read p.191 through 193

read sec. 2 up to p.155

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