10.14) The results obtained by a single pass through an image of some 2-D kernels can be achieved also by two passes using 1-D kernels. For example, the same result of using a 3 x 3 smoothing kernel...

Extracted text: 10.14) The results obtained by a single pass through an image of some 2-D kernels can be achieved also by two passes using 1-D kernels. For example, the same result of using a 3 x 3 smoothing kernel with coefficients 1/9 can be obtained by a pass of the kernel [1 1 1] through an image, followed by a pass of the result with the kernel [1 1 1]'. The final result is then scaled by 1/9. Show that the response of Sobel kernels (Fig. 10.14) can be implemented similarly by one pass of the differencing kernel [-1 0 1] (or its vertical coun- terpart) followed by the smoothing kernel [1 2 1] (or its vertical counterpart). Fig. 10.14) a b c de f g ** Roberts -1 1- Prewitt -- -2 -2 21 1. 2. --1 Sobel