Question: In digital image processing, first-order derivatives can be approximated by the spatial differences g x =( f(x, y) x )=f(x+1,y)-f(x, y) and g y =(

In digital image processing, first-order derivatives can be approximated by the spatial differences g_x=(f(x, y) differences gx=(f(x, y)x)=f(x+1,y)-f(x, y) and gy=(f(x, y)/y)=f(x, y+1)-f(x, y). a. Find the _x)=f(x+1,y)-f(x, y) and g_y=( equivalent filter transfer functions Hx(u, v) and Hy(u, v) in the frequency f(x, y)/ domain. b. Show that these are highpass filter transfer functions. (Hint: Study y)=f(x, y+1)-f(x, y).

a. Find the equivalent filter transfer functions Hx(u, v) and Hy(u, v) in the frequency domain.

b. Show that these are highpass filter transfer functions. (Hint: Study the solution to Problem 4.51 U.)

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