In class, we introduced 2D discrete space convolution Consider an input image I[i; j] and an m X n filter F[i: j]. The 2D convolution [ + F is defined as: (I + F)[i,j] = [[i k, j - 1]F[k, 1]. Hint: The above operation is run for each pixel (i; j) of the result. (a) Convolve the following I and F. Assume we use zero-padding where necessary. 2 0 1] F- 1 -1 2 Important: DO NOT use MATLAB for this question. Please show all necessary steps to receive full credit. (b) Note that the F given in (2) is separable; that is, it can be written as a product of two 1D filters: F F1F2. Here, we have: F1 F2 = (1 - 1) = 0 Compute (I * Fi) and (I * F) * F2, i.e. first perform 1D convolution on each column, followed by another 1D convolution on each row. Important: DO NOT use MATLAB for this question. Please show all necessary steps to receive full credit. In class, we introduced 2D discrete space convolution Consider an input image I[i; j] and an m X n filter F[i: j]. The 2D convolution [ + F is defined as: (I + F)[i,j] = [[i k, j - 1]F[k, 1]. Hint: The above operation is run for each pixel (i; j) of the result. (a) Convolve the following I and F. Assume we use zero-padding where necessary. 2 0 1] F- 1 -1 2 Important: DO NOT use MATLAB for this question. Please show all necessary steps to receive full credit. (b) Note that the F given in (2) is separable; that is, it can be written as a product of two 1D filters: F F1F2. Here, we have: F1 F2 = (1 - 1) = 0 Compute (I * Fi) and (I * F) * F2, i.e. first perform 1D convolution on each column, followed by another 1D convolution on each row. Important: DO NOT use MATLAB for this question. Please show all necessary steps to receive full credit