Sharpening

Sharpening, as smoothing, is done thru a convolution with the following matrix

$\displaystyle \left[\vphantom{ \matrix {-1 & -2 & -1 \cr
-2 & 10 & -2 \cr
-1 & -2 & -1 } }\right.$$\displaystyle \matrix {-1 & -2 & -1 \cr
-2 & 10 & -2 \cr
-1 & -2 & -1 } $$\displaystyle \left.\vphantom{ \matrix {-1 & -2 & -1 \cr
-2 & 10 & -2 \cr
-1 & -2 & -1 } }\right]$$\displaystyle \ceqno$