Suppose that an image f(x, y)is convolved with a mask of size n × n (with coefficients 1/n...

Suppose that an image f(x, y)is convolved with a mask of size n × n (with coefficients 1/n2) to produce a smoothed image .

(a) Derive an expression for edge strength (edge magnitude) of the smoothed image as a function of mask size. Assume for simplicity that n is odd and that edges are obtained using the partial derivatives

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(b) Show that the ratio of the maximum edge strength of the smoothed image to the maximum edge strength of the original image is 1/n. In other words, edge strength is inversely proportional to the size of the smoothing mask.