1. (30 points) You are given the following kernel and image: 0 0 0 0 1 2 1 0 0 1 0 0 2 4 2 f = 0 1 0 2 0 0 1 0 0 0 0 (a). Compute the convolution of w and f. Show the details of your computations when the kernel is centered on point (2, 3) of f; and then show the final full convolution result. (b). If the kernel is separable, then the kernel can be expressed as product of two vectors, W = v, V2 . Decide whether the kernel w is separable. (c). Prove that if the kernel is separable, w * f = v1 * (v2 * f)