Sobel Filter
[Separable filter](https://texonom.com/separable-filter-70c9a94159c64cbe85080f9ddf586c47) 


$$Spober\; Filter = Blurring \; \ast \; 1D \; Derivative \; filter$$
### Horizontal Sober Filter $S_x$
$$\begin {pmatrix}1 & 0 & -1 \\2 & 0 & -2 \\1 & 0 & -1\end {pmatrix}=\begin {pmatrix}1  \\2  \\1 \end {pmatrix}\ast\begin {pmatrix}1 & 0 &  -1 \\\end {pmatrix}$$
가로성분 1d derivative 들어가니까


### Vertical Sobel Filter $S_y$
$$\begin {pmatrix}1 & 2 & 1 \\0 & 0 & 0 \\1 & -2 & -1\end {pmatrix}=\begin {pmatrix}1  \\0  \\-1 \end {pmatrix}\ast\begin {pmatrix}1 & 2 &  1 \\\end {pmatrix}$$
세로성분 1d derivative 들어가니까

![](https://www.notion.so/image/https%3A%2F%2Fs3-us-west-2.amazonaws.com%2Fsecure.notion-static.com%2F8ec643fa-4b70-4c76-bd2d-8c416013851d%2FUntitled.png?table=block&id=0a0ece35-712f-4f25-95db-f04b74c32b34&cache=v2)
모양때문에 이름 착각하지 말기



### resultpa
$$I_x = \frac{\partial I}{\partial x} $$
$$I_y = \frac{\partial I}{\partial y}$$




