I. You are given the following kernel and image: U U [l U U l 2 l U U l U U u: 2 a1 2 f U U 1 U U l 2 l U U l U U U U U U U {a} Use the mechanics of' spatial lter shown in lecture":II slides #5. when the kernel is centered at point {2. 3} {2nd row. 3rd col] of'the image shown above. Show specific values of'w and f'. {b} Compute the convolution, w 1r f. Show the details of' your computations when the kernel is centered on point {2. 3) off; and then show the nal full convolution result. {c} Compute the correlation, w'i'rf. Show the details of your computations when the kernel is centered on point {2. 3) off; and then show the nal full correlation n result. {d} If the kernel is separable1 then the kernel can he expressed as product of two vectors. w = Vlva- Decide whether the kernel w is separable. {e} Prove that :if'the kernel is separable. w it f = 111 1r (1J2 1r f]. Image origin Kernel origin Magnified view showing filter kernel Filter kernel coefficients and corresponding pixels in the image Mechanics of Image pixels Spatial filter w (-1, -1) w(-1,0) w(-1,1) Image f w (0, -1) w (0,0) w (0,1) Filter kernel, w(s,f) g(x, y) = w(-1, - 1)f(x - 1, y - 1) + w(-1, 0)f(x - 1, y) + ... +w(0, 0)f(x, y) + ... + w(1, 1)f(x + 1, y + 1) w (1,-1) w (1,0) w (1,1) f(x - 1, y -1) f(x-1,y) f(x -1,y+ 1) Kernel coefficients f(x,y - 1) f(x,y) (x,y + 1) f(x + 1, y-1) f(x +1,y) f(x +1,y+1) Pixel values under kernel when it is centered on (x, y)