Answer Happy

Question B. 1 a) Consider the following 3 x 3 spatial mask: 0 -1 0 -1 4-1 0 -1 0 Figure 2 i) Find the equivalent filter, H(u,v), in the frequency domain. Express H(u, v) in terms of sinusoidal functions. [8 marks] ii) Show that your result is a high pass filter. Justify your answer. [5 marks] b) Suppose that you filter an image f(x,y) with a spatial filter mask w(x,y) using convolution, where the mask is smaller than the image in both spatial directions. i) Show the important property that, if the coefficients of the mask sum to zero, then the sum of all the elements in the resulting convolution array (filtered image) will be zero also (you may ignore computational inaccuracies). Also, you may assume that the border of the image has been padded with the appropriate number of zeros. [8 marks) ii) Would the result to (i) be the same if the filtering is implemented using correlation? Justify your answer. [4 marks] [25 marks]