2.3 Test Results
Figure 1 shows an image of the national monument "Anping Fort" in Tainan, Taiwan, and its gradient images computed by the Sobel operators (Gonzalez and Woods, 1993) and by the Daubechies operators of order N=3 and N=10, respectively. In the same manner as common practice, the gradient is approximated with absolute values (Gonzalez and Woods, 1993). In all computations of gradients, all operators are normalized so that
åbm=1.
Figure 2 expresses the mean, RMS (=root mean square) value, and maximum of gradients of the "Anping Fort" image. Apparently, the gradients computed by the Daubechies operators of N=3 (1) 10 have larger mean, RMS and maximal gradients than the ones determined by the Sobel operators. There exists a distinct effect. For example, Figure 3 illustrates an image of a Chinese character 'dragon' and its gradient images. Daubechies operators can extract much finer edges than the Sobel operators. Moreover, the center lines of all edges determined by both Daubechies and Sobel operators are the same. Figure 4 illustrates an example. The edges computed by the Daubechies operator of order N=3 are located in the centers of the edges computed by the Sobel operators.
In other words, the proposed Daubechies operators are new ones for gradient computation. Test results show that they can extract unbiased and finer edges, e.g. than the Sobel operators.
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Figure 1. (a) an image of Anping Fort in Tainan, Taiwan, and its gradient images computed by the Sobel operators (b), the Daubechies operator of order N=3 (c) and N=10 (d), respectively.
Figure 2. mean values (left), RMS (middle) and maximum (right) of gradients of the "Anping Fort" image shown in Figure 1 computed by the Daubechies operator of N = 3 (1) 10, where the square denotes the ones determined by the Sobel operators.
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Figure 3. (a) an image of a Chinese character "dragon" and its gradient images computed by the Sobel operator (b), Daubechies operators of N=3 (c) and N=10 (d), respectively.
Figure 4. The edges computed by the Daubechies operator of order N=3 (white center lines) are located in the center of the edges computed by the Sobel operators (dark boundary lines).
