1-Convolve the subimage shown below with a 3x3 mean filter. What is the output of the convolution at the center entry of the subimage? What about if

1-Convolve the subimage shown below with a 3x3 mean filter. What is the output of the convolutionat the center entry of the subimage? What about if you use a 3x3 median filter?4 1 6 1 33 2 7 7 22 5 7 3 71 4 7 1 30 1 6 4 42-Consider the sub-image shown above. Find the gradient magnitude andgradient direction at the center entry using the following operators. (Hint: Calculate forjust the center pixel not the entire sub-image)(a) The Prewitt operator, and(b) The Sobel operator.3- (20 pts) Compare the time complexity of convolution with a n x n kernel when using:(a) direct convolution with the 2-D mask, and(b) a separable kernel.4- (20 pts) Prove the following properties of the Gaussian function,(a) Symmetry: G(x) =G(-x)(b) Product of two Gaussians is a Gaussian: G1(x) xG2(x)= G(x)5- (20 pts) Generate the mask for 255x 2G(x, y), for _ = 1. Truncate all the mask valuesto the nearest integer (Hint: 1- Write a program. 2-2 is the Laplacian Operator