3 Image Enhancement 3.6.1一阶和二阶导数 first-and-second-order derivatives- >Sharpening filter is based on the first second derivative The first order derivative af(x) lim f(+Ax)-f() Ox △x→0 △x ,x∈R △x=1 df(x) 一阶导数近似： =f(x+1)-f(x) Ox ,x∈N 二阶导数近似： o Ox2 =f'(x)-f'(x-) =[f(x+I)-f(x)]-[f(x)-f(x-1)] =f(x+1)+f(x-1)-2f(x)3 Image Enhancement 3.6.1 一阶和二阶导数 first- and second-order derivatives Sharpening filter is based on the first & second derivative 0 0 0 0 ( ) ( ) ( ) lim x x x f x f x x f x x x           The first order derivative： , x 一阶导数近似: ( ) ( 1) ( ) f x f x f x x      二阶导数近似: 2 2 f x f ( ) ( 1) f x    x          f x f x f x ( 1) ( 1) 2 ( )        f x f x f x f x ( 1) ( ) ( ) ( 1)    , x  x 1