(a) (5 points) Given the folluwing two filters for linear filtering. discuss their purposes respoctivoly: (b) (.) points) Denote the input pixel value of an input image f at (x,y) as f(x,y). the origin of the image is at the top-left corner. the x and y axes correspond to the rertical and hurizontal axes. respectively. Find the two formulas of generating output image g with output pixel values g(x,y) by conducting linear filtering on the input inage f with filters in (a). (c) (10 points) Recall that we can approxinate 2nd-oreler derivatives of an input image f w.r.t. x as x22f(x,y)xxf(x+x,y)f(x,y)xf(x,y)f(xx,y)(Equalityholdswhenx(0)x2f(x+x,y)2f(x,y)+f(xx,y)12f(x+1)2f(x)+f(x1)(bysettingx=1)=f(x+1)2f(x)+f(x1) Find how to approximate xy2f