Compute the Sobel gradient components without using a computer for the 11x11 input image f(m,n). For 0 m, n 10, f(m,n) has a value of 100 when both m and n are greater than or equal to 5, and otherwise has a value of 0. a.) Convolve f(m,n) with the Sobel filter H1 = [1 2 1; 0 0 0; -1 -2 -1] to produce valid output of gl(m,n). Find the values of indices (m, n) where gl is not zero. For these indices find the value of gl. b.) Repeat (a) using H2 = [ 1 0 -1; 2 0 -2; 1 0 -1] to produce g2(m,n). c.) Interpret the vector [g1(m, n), g2(m, n)] as a gradient indicating a magnitude and a direction of change of the image intensity at (m,n). Using the values computed in (a) and (b), compute the magnitude of the gradient at each pixel.