6. You are given the following derivative filter: 111000111 This filter represents an approximation of the derivative filter in the horizontal direction. (a) [5 points] Compute the convolution result at the pixels marked in bold below, i.e., [0,0],[2,3],[2,6], [4,3] and [4,6]. The origin is located at the top-left corner with coordinate [0,0]. Assume zero padding is used along the image borders. (b) [5 points] Compute the gradient magnitude at the pixels marked in bold. Assume the same derivative filter approximation used for the horizontal direction is used for the vertical direction. Show all work