(a) Suppose that you filter an image, f(x, y), with a spatial filter mask, w(x, y), using...

(a) Suppose that you filter an image, f(x, y), with a spatial filter mask, w(x, y), using convolution, as defined in Eq. (3.4-2), where the mask is smaller than the image in both spatial directions. 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.

(3.4-2)

---

(b) Would the result to (a) be the same if the filtering is implemented using correlation, as defined in Eq. (3.4-1)?

(3.4-1)