3. Let be an image with 1111 pixels. In the center of the image is a square of 55 pixels. The gray level of the background is 100 and the gray level of the square is 0 . a) represent the image as an indexed one (aka write the matrix that represents the image) (1point) b) Compute the result of a linear filter with the kernel below (the origin is the middle pixel). Explain your result. What is this filter useful for? (2 points) \[ \begin{array}{rrr} 0 & -1 & 0 \\ -1 & 4 & -1 \\ \cline { 2 - 3 } 0 & -1 & 0 \end{array} \] c) Compute the result of a median filter with 33 centered neighbourhood ( 2 points) d) Compute the result of the magnitude of edges given by the compass operator for this image. Take into account that the image is not noisy. Explain your result. ( 5 points)