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122 3 Image processing

Name Kernel Transform Plot
1.0
0.8
0.6
0.4
1 1 0.2
box-3 3 1 1 1 3 (1 + 2 cos ω) 0.0
0 0.1 0.2 0.3 0.4 0.5
-0.2
-0.4
1.0
0.8
0.6
0.4
1 1 0.2
box-5 5 1 1 1 1 1 5 (1 + 2 cos ω + 2 cos 2ω) 0.0
0 0.1 0.2 0.3 0.4 0.5
-0.2
-0.4
1.0
0.8
0.6
0.4
1 1 2 1 1 0.2
linear 4 2 (1 + cos ω) 0.0
0 0.1 0.2 0.3 0.4 0.5
-0.2
-0.4
1.0
0.8
0.6
0.4
1 1 4 6 4 1 1 2 0.2
binomial 16 4 (1 + cos ω) 0.0
0 0.1 0.2 0.3 0.4 0.5
-0.2
-0.4
1.0
0.8
0.6
0.4
1 0.2
Sobel 2 −1 0 1 sin ω 0.0
0 0.1 0.2 0.3 0.4 0.5
-0.2
-0.4
1.0
0.8
0.6
0.4
1 1 0.2
corner 2 −1 2 −1 2 (1 − cos ω) 0.0
0 0.1 0.2 0.3 0.4 0.5
-0.2
-0.4

Table 3.3 Fourier transforms of the separable kernels shown in Figure 3.14.