The Sobel filter is a set of two convolution filters used to detect horizontal and vertical edges in images.

The horizontal filter is

$$\left[\begin{array}{ccc}1& 0& -1\\ 2& 0& -2\\ 1& 0& -1\end{array}\right]$$

and the vertical filter is

$$\left[\begin{array}{ccc}1& 2& 1\\ 0& 0& 0\\ -1& -2& -1\end{array}\right]$$