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and 2 show CT and MR image sets, respectively, selected to test the performance of wavelet filters on images with different modality, anatomy, technique of acquisition, and pixel size.

The smoothness of an image f(x, y) can be quantified using the autocorrelation function defined as c(m, n) = YY1 f*(x, y) -f (x + m, y + n),

where * stands for the complex conjugate, and m and n are integers that define the spacing (lag) between pixels in the x and y directions, respectively. The correlation coefficients are defined as cc(m, n)

Figure 7 shows the correlation coefficients as a function of m when n = 0, i.e., cc(m, 0), for the sample images stated in Tables 1 and 2. A larger correlation indicates that adjacent pixels are more likely to have similar values. Images with higher correlation coefficients generally have lower high-frequency components, have fewer sharp edges, and appear smoother.

For CT images (Fig. 7a) the correlation coefficients of the spine and abdomen images are much larger than those of the head and chest images. Therefore, spine and abdomen images are comparatively smoother and have lower high-frequency components. In general, an image with a smaller pixel size has higher correlation coefficients than the one with a larger pixel size for the same anatomy. For example, the chest image with 0.66-mm pixel size (chest.66) has higher correlation coefficients than the chest image with 0.94-mm pixel size (chest.94) in Fig. 7a.

For most MR images (Fig. 7b), the correlation coefficients are very close in value when the shift, m, is small. In general, for the same pixel shift, CT images have larger correlation

FIGURE 7 Correlation coefficients of sample images: (a) CT, (b) MR.

coefficients than MR images because CT images are often smoother than MR images.

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